Diana T. Stoeva
In this paper we consider perturbation of X_d-Bessel sequences, X_d-frames, Banach frames, atomic decompositions and X_d-Riesz bases in separable Banach spaces. Equivalence between some perturbation conditions is investigated.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We extend the Paley-Wiener pertubation theory to linear operators mapping a subspace of one Banach space into another Banach space.
In this paper we prove that if (A,π) is an amenable Banach algebra and if ρis another Banach algebra multiplication on A such that the difference between ρand and πis less than 1/11, then (A, ρ) is also amenable.
Paley-Wiener theorem for frames for Hilbert spaces, Banach frames, Schauder frames and atomic decompositions for Banach spaces are known. In this paper, we derive Paley-Wiener theorem for p-approximate Schauder frames for separable Banach spaces. We show that our results give Paley-Wiener theorem for frames for Hilbert spaces.
Perturbation of Schauder frames and besselian Schauder frames in Banach spaces
本文研究了Banach空间中Schauder框架与besselian Schauder框架在扰动下的稳定性，其结果与Heil的研究密切相关。
We consider a perturbation determinant for pairs of nonpositive (in a sense of Komatsu) operators on Banach space with nuclear difference and prove a generalization of the important formula for the logarithmic derivative of this determinant. To this end the Frechet differentiability of operator monotonic (negative complete Bernstein) functions of negative and nonpositive operators on Banach spaces is investigated. The results may be regarded as a contribution to the Hirsch functional calculus.
We show that the perturbation class for the upper semi-Fredholm operators between two Banach spaces X and Y coincides with the strictly singular operators when X is subprojective and that the perturbation class for the lower semi-Fredholm operators coincides with the strictly cosingular operators when Y is superprojective. Similar results were previously obtained under stronger conditions for X and Y.
The wark is a contribution to the functional calculus constructed by of the author and A. A. Atvinovskii of closed operators on Banach spaces. The calculus is based on Markov and related functions as symbols. Estimates of bounded perturbations of operator functions with respect to general operator ideal norms, operator Lipschitzness, moment inequality, Freshet operator differentiability, and Livshitz-Krein trace formulae have been considered.
Perturbation of the mapping and solvability theorems in Banach space
该研究针对Banach空间上连续映射的扰动问题，通过分析映射局部性质、与光滑映射局部比较等方法，探究几类方程与包含关系的可解性，同时还研究了不同的混合问题。
One-sided Drazin inverses in Banach algebras and perturbations of B-Fredholm spectra
本文在Banach代数中引入单边（广义）Drazin逆，刻画Banach空间上相应可逆算子，并利用单边Drazin可逆谱给出B-Fredholm谱的扰动刻画，推广了经典Fredholm理论。
It is known that Dobrushin's ergodicity coefficient is one of the effective tools in the investigations of limiting behavior of Markov processes. Several interesting properties of the ergodicity coefficient of a positive mapping defined on ordered Banach space with a base have been studied. In this paper, we consider uniformly mean ergodic and asymptotically stable Markov operators on ordered Banach spaces. In terms of the ergodicity coefficient, we prove uniform mean ergodicity criterion in terms of the ergodicity coefficient. Moreover, we develop the perturbation theory for uniformly asympto…
We extend an example of B. Aupetit, which illustrates spectral discontinuity for operators on an infinite dimensional separable Hilbert space, to a general spectral discontinuity result in abstract Banach algebras. This can then be used to show that given any Banach algebra, $Y$, one may adjoin to $Y$ a non-commutative inessential ideal, $I$, so that in the resulting algebra, $A$, the following holds: To each $x\in Y$ whose spectrum separates the plane there corresponds a perturbation of $x$, of the form $z=x+a$ where $a\in I$, such that the spectrum function on $A$ is discontinuous at $z$.
The paper deals with multidimensional Bochner-Phillips functional calculus. In the previous paper by the author bounded perturbations of Bernstein functions of several commuting semigroup generators on Banach spaces where considered, conditions for Lipschitzness and estimates for the norm of commutators of such functions where proved. Also in the one-dimensional case the Frechet differentiability of Bernstein functions of semigroup generators on Banach spaces where proved and a generalization of Livschits-Kreĭn trace formula derived. The aim of the present paper is to prove the Frechet differe…
We give a simple definition of a spectral shift function for pairs of nonpositive operators on Banach spaces and prove trace formulas of Lifshitz-Kre\uın type for a perturbation of an operator monotonic (negative complete Bernstein) function of negative and nonpositive operators on Banach spaces induced by nuclear perturbation of an operator argument. The Lipschitzness of such functions is also investigated. The results may be regarded as a contribution to a perturbation theory for Hirsch functional calculus.
Quasi-compactness and uniform stabilization on general Banach spaces under $θ$-subordinate perturbations of semigroup generators
本文证明在一般Banach空间上，解析半群在沿轨道紧的$\ heta$-从属扰动下保持拟紧性和一致指数稳定性，并推广至Crandall-Pazy半群及立即可微半群，最后通过反例说明$A$-有界扰动下稳定性可能缺失。
We prove a very general theorem concerning the estimation of the expression $\|T(\frac{a+b}{2}) - \frac{Ta+Tb}{2}\|$ for different kinds of maps $T$ satisfying some general perurbated isometry condition. It can be seen as a quantitative generalization of the classical Mazur-Ulam theorem. The estimates improve the existing ones for bi-Lipschitz maps. As a consequence we also obtain a very simple proof of the result of Gevirtz which answers the Hyers-Ulam problem and we prove a non-linear generalization of the Banach-Stone theorem which improves the results of Jarosz and more recent results of D…
A note on the stability of Arens products under small perturbations of multiplication
本文研究Banach代数乘法小扰动对双对偶上Arens积的影响，证明Arens不规则性在足够小扰动下稳定，且等价于一致代数的Banach函数代数的Arens正则性在小扰动下保持稳定。
A remarkable result of Molnár [Proc. Amer. Math. Soc., 126 (1998), 853-861] states that automorphisms of the algebra of operators acting on a separable Hilbert space is stable under "small" perturbations. More precisely, if $ϕ,ψ$ are endomorphisms of $\mathcal{B}(\mathcal{H})$ such that $\|ϕ(A)-ψ(A)\|<\|A\|$ and $ψ$ is surjective then so is $ϕ$. The aim of this paper is to extend this result to a larger class of Banach spaces including $\ell_p$ and $L_p$ spaces ($1<p<+\infty$). En route to the proof we show that for any Banach space $X$ from the above class all faithful, unital, separable, ref…
We introduce a new concept of perturbation of closed linear subspaces and operators in Banach spaces called uniform lambda-adjustment which is weaker than perturbations by small gap, operator norm, q-norm, and K2-approximation. In arbitrary Banach spaces some of the classical Fredholm stability theorems remain true under uniform lambda-adjustment, while other fail. However, uniformly lambda-adjusted subspaces and linear operators retain their (semi--)Fredholm properties in a Banach space which dual is Fréchet-Urysohn in weak* topology. We also introduce another concept of perturbation called u…
We consider the effect of perturbations to a quasi-linear parabolic stochastic differential equation set in a UMD Banach space $X$. To be precise, we consider perturbations of the linear part, i.e. the term concerning a linear operator $A$ generating an analytic semigroup. We provide estimates for the difference between the solution to the original equation $U$ and the solution to the perturbed equation $U_0$ in the $L^p(Ω;C([0,T];X))$-norm. In particular, this difference can be estimated $|| R(λ:A)-R(λ:A_0) ||$ for sufficiently smooth non-linear terms. The work is inspired by the desire to pr…
Given a Banach space operator $A$, the isolated eigenvalues $E(A)$ and the poles $Π(A)$ (resp., eigenvalues $E^a(A)$ which are isolated points of the approximate point spectrum and the left ploles $Π^a(A)$) of the spectrum of $A$ satisfy $Π(A)\subseteq E(A)$ (resp., $Π^a(A)\subseteq E^a(A)$), and the reverse inclusion holds if and only if $E(A)$ (resp., $E^a(A)$) has empty intersection with the B-Weyl spectrum (resp., upper B-Weyl spectrum) of $A$. Evidently $Π(A)\subseteq E^a(A)$, but no such inclusion exists for $E(A)$ and $Π^a(A)$. The study of identities $E(A)=Π^a(A)$ and $E^a(A)=Π(A)$, an…
We are concerned with surjectivity of perturbations of maximal monotone operators in non-reflexive Banach spaces. While in a reflexive setting, a classical surjectivity result due to Rockafellar gives a necessary and sufficient condition to maximal monotonicity, in a non-reflexive space we characterize maximality using a ``enlarged'' version of the duality mapping, introduced previously by Gossez.
The notion of retro Banach frame with the help of b-linear functional in n-Banach spaces is being presented. Some properties related to the construction of new retro Banach frame in n-Banach space have been studied. In n-Banach spaces, some perturbation results of retro Banach frame have been discussed. Finally, we give a condition in which finite sum of retro Banach frames is a retro Banach frame in n-Banach space.
We present partial results to the following question: Does every infinite dimensional Banach space have an infinite dimensional subspace on which one can define an operator which is not a compact perturbation of a scalar multiplication?
We prove a Desch-Schappacher type perturbation theorem for one-parameter semigroups on Banach spaces which are not strongly continuous for the norm, but possess a weaker continuity property. In this paper we chose to work in the framework of bi-continuous semigroups. This choice has the advantage that we can treat in a unified manner two important classes of semigroups: implemented semigroups on the Banach algebra $\mathscr{L}(E)$ of bounded, linear operators on a Banach space $E$, and semigroups on the space of bounded and continuous functions over a Polish space induced by jointly continuous…
Concepts of g-fusion frame and gf-Riesz basis in a Hilbert to a Banach space is being presented. Some properties of g-fusion frame and gf-Riesz basis in Banach space have been developed. We discuss perturbation results of g-fusion frame in a Banach space. Finally, we construct g-p-fusion frames in Cartesian product of Banach spaces and tensor product of Banach spaces.
Let $M_{C}=\left(\begin{array}{cc}A&C\\0&B\\\end{array} \right)$ is a 2-by-2 upper triangular operator matrix acting on the Banach space $X\oplus Y$ or Hilbert space $H\oplus K$. For the most import spectra such as spectrum, essential spectrum and Weyl spectrum, the characterizations of the perturbations of $M_{C}$ on Banach space have been presented. However, the characterization for the Browder spectrum on the Banach space is still unknown. The goal of this paper is to present some necessary and sufficient conditions for $M_C$ to be Browder for some $C\in B(Y,X)$ by using an alternative appr…
In this paper we show that the concept of maximal $L^p$-regularity is stable under a large class of unbounded perturbations, namely Staffans-Weiss perturbations. To that purpose, we first prove that the analyticity of semigroups is preserved under this class of perturbations, which is a necessary condition for the maximal regularity. In UMD spaces, $\mathcal{R}$-boundedness conditions are exploited to give conditions guaranteing the maximal regularity. For non-reflexive Banach space, a condition is imposed to the Dirichlet operator associated to the boundary value problem to prove the maximal …
In this paper Hilbert spaces are characterized among Banach spaces in terms of transitivity with respect to nicely behaved subgroups of the isometry group. For example, the following result is typical here: If X is a real Banach space isomorphic to a Hilbert space and convex-transitive with respect to the isometric finite-dimensional perturbations of the identity, then X is already isometric to a Hilbert space.
The application of generalized inverses is usually neglected in pure mathematical research. However, it is very effective for this paper. We expand the famous matrix rank theorem due to R. Penrose to operators between Banach paces. Therefore a modern perturbation analysis of generalized inverses is built. Hereby, we find and prove a complete rank theorem in advanced calculus. So a complete answer to the rank theorem problem presented by M. S. Berger is given. Applying the co-final set and the perturbation analysis of generalized inverses we prove the Frobenius theorem in Banach space, in the p…
A strong inspiration for studying perturbation theory for fractional evolution equations comes from the fact that they have proven to be useful tools in modeling many physical processes. In this paper, we study fractional evolution equations of order $α\in (1,2]$ associated with the infinitesimal generator of an operator fractional cosine function generated by bounded time-dependent perturbations in a Banach space. We show that the abstract fractional Cauchy problem associated with the infinitesimal generator $A$ of a strongly continuous fractional cosine function remains uniformly well-posed …
Concept of p-frame with the help of b-linear functional in the case of n-Banach space is being presented and its few properties, one of them, Cartesian product of two p-frames again becomes a p-frame, have been discussed. Finally, the perturbation results and the stability of p-frame in n-Banach space with respect to b-linear functional are being studied.
New Generalized Dual Banach Frames
本文系统研究了Banach空间中的g-对偶Banach框架，建立了其存在条件，探讨了与其他广义对偶概念的关系，并证明了其在有界扰动下的稳定性。
A variant of the abstract Cauchy-Kovalevskaya theorem is considered. We prove existence and uniqueness of classical solutions to the nonlinear, non-autonomous initial value problem \[ \frac{du(t)}{dt} = A(t)u(t) + B(u(t),t), \ \ u(0) = x \] in a scale of Banach spaces. Here $A(t)$ is the generator of an evolution system acting in a scale of Banach spaces and $B(u,t)$ obeys an Ovcyannikov-type bound. Continuous dependence of the solution with respect to $A(t)$, $B(u,t)$ and $x$ is proved. The results are applied to the Kimura-Maruyama equation for the mutation-selection balance model. This yiel…
In this paper, we prove that the existence of an $\varepsilon$-isometry from a separable Banach space $X$ into $Y$ (the James space or a reflexive space) implies the existence of a linear isometry from $X$ into $Y$. Then we present a set valued mapping version lemma on non-surjective $\varepsilon$-isometries of Banach spaces. Using the above results, we also discuss the rotundity and smoothness of Banach spaces under the perturbation by $\varepsilon$-isometries.
Global folds between Banach spaces are obtained from a simple geometric construction: a Fredholm operator $T$ of index zero with one dimensional kernel is perturbed by a compatible nonlinear term $P$. The scheme encapsulates most of the known examples and suggests new ones. Concrete examples rely on the positivity of an eigenfunction. For the standard Nemitskii case $P(u) = f(u)$ (but $P$ might be nonlocal, non-variational), $T$ might be the Laplacian with different boundary conditions, as in the Ambrosetti-Prodi theorem, or the Schrödinger operators associated with the quantum harmonic oscill…
In this paper, we propose to define the concept of family of local atoms and then we generalize this concept to the atomic system for operator in Banach spaces by using semi-inner product. We also give a characterization of atomic systems leading to obtain new frames. In addition, a reconstruction formula is obtain. Next, some new results are established. The characterization of atomic systems allows us to state some results for sampling theory in semi-inner product reproducing kernel Banach spaces. Finally, having used frame operator in Banach spaces, new perturbation results are established.
We extend and generalize the result of Kalton and Swanson ($Z_2$ is a symplectic Banach space with no Lagrangian subspace) by showing that all higher order Rochgberg spaces $\mathfrak R^{(n)}$ are symplectic Banach spaces with no Lagrangian subspaces. The nontrivial symplectic structure on even spaces is the one induced by the natural duality; while the nontrivial symplectic structure on odd spaces requires perturbation with a complex structure. We will also study symplectic structures on general Banach spaces and, motivated by the unexpected appearance of complex structures, we introduce and …
Skew-adjoint linear relatioins between Banach spaces
本文证明了辛 Banach 空间中极大迷向子空间扰动的稳定性，以及指标为 0 的斜伴随 Fredholm 关系核的模 2 维数稳定性，并刻画了其路径连通分支。
In this work, we prove the existence and uniqueness of $μ$-pseudo almost automorphic solutions for some class of semilinear nonautonomous evolution equations of the form: $ u'(t)=A(t)u(t)+f(t,u(t)),\; t\in\mathbb{R} $ where $ (A(t))_{t\in \mathbb{R}} $ is a family of closed densely defined operators acting on a Banach space $X$ that generates a strongly continuous evolution family which has an exponential dichotomy on $\mathbb{R}$. The nonlinear term $f: \mathbb{R} \times X \longrightarrow X$ is just $μ$-pseudo almost automorphic in Stepanov sense in $t$ and Lipshitzian with respect to the sec…
An operator $T \in \mathcal{B}(X)$ defined on a Banach space $X$ satisfies property $(gb)$ if the complement in the approximate point spectrum $σ_{a}(T)$ of the upper semi-B-Weyl spectrum $σ_{SBF_{+}^{-}}(T)$ coincides with the set $Π(T)$ of all poles of the resolvent of $T$. In this note we continue to study property $(gb)$ and the stability of it, for a bounded linear operator $T$ acting on a Banach space, under perturbations by nilpotent operators, by finite rank operators, by quasi-nilpotent operators commuting with $T$. Two counterexamples show that property $(gb)$ in general is not prese…
We find a natural class of transformations ("flattened perturbations") of a norming M-basis in a Banach space X, which give a strong norming M-basis in X. This simplifies and generalizes the positive answer to the "strong M-basis problem" solved by P. Terenzi. We also show that in general one cannot achieve uniformly minimality applying standard transformations to a given norming M-basis, despite of the existence in X a uniformly minimal strong M-bases.
Perturbation analysis of bounded homogeneous generalized inverses on Banach spaces
研究Banach空间上有界线性算子T的有界齐次广义逆T^h和拟线性投影广义逆T^H的扰动问题，并应用于Moore-Penrose度量广义逆T^M的表示与扰动，推广了线性算子广义逆的经典结果。
We construct a Bourgain-Delbaen $\mathscr{L}_\infty$-space $\mathfrak{X}_{Kus}$ with strongly heterogenous structure: any bounded operator on $\mathfrak{X}_{Kus}$ is a compact perturbation of a multiple of the identity, whereas the space $\mathfrak{X}_{Kus}$ is saturated with unconditional basic sequences.
We answer the question of W.T. Gowers, giving an example of a bounded operator on a subspace of Gowers unconditional space which is not a strictly singular perturbation of a restriction of a diagonal operator. We make some observations on operators in arbitrary tight by support Banach space, showing in particular that in such space no two isomorphic infinitely dimensional subspaces form a direct sum.
The main purpose of this paper is to investigate the concept of maximal $L^p$-regularity for perturbed evolution equations in Banach spaces. We mainly consider three classes of perturbations: Miyadera-Voigt perturbations, Desch-Schappacher perturbations, and more general Staffans-Weiss perturbations. We introduce conditions for which the maximal $L^p$-regularity can be preserved under these kind of perturbations. We give examples for a boundary perturbed heat equation in $L^r$-spaces and a perturbed boundary integro-differential equation. We mention that our results mainly extend those in the …
Motivating the perturbations of frames in Hilbert and Banach spaces, in this paper we introduce the invariance of Fréchet frames under perturbation. Also we show that for any Fréchet spaces, there is a Fréchet frame and any element has a series expansion.
On the stability of the Bishop's property($β$) under compact perturbations
本文证明了Banach空间上算子的Bishop性质($\beta$)、分解性质($\delta$)及可分解性在拟幂零、紧和代数可交换扰动下保持稳定，推进了局部谱理论中开放问题的研究。
The main purpose of this paper is to treat semigroups properties, like norm continuity, compactness and differentiability for perturbed semigroups in Banach spaces. In particular, we investigate three large classes of perturbations, Miyadera-Voigt, Desch-Schappacher and Staffans-Weiss perturbations. Our approach is mainly based on feedback theory of Salamon-Weiss systems. Our results are applied to abstract boundary integro-differential equations in Banach spaces.
Frobenius Theorem in Banach Space and Generalized Inverse Analysis Method of Operators Under Small Perturbations
本文在Banach空间中推广了Frobenius定理，通过定义余尾集和利用广义逆分析方法，解决了无限维子空间的可积性问题，并应用于微分方程和极值原理等领域。
The characterizations of the stable perturbation of a closed operator by a linear operator in Banach spaces
研究闭算子T在广义逆T^+存在时，线性扰动δT使得T+δT保持广义逆稳定的条件，推广了Huang在Linear Algebra and its Applications中的主要结果。
Perturbation analysis for the generalized inverses with prescribed idempotents in Banach algebras
本文研究了Banach代数中具有指定幂等元的广义逆的扰动表达式，并给出了当幂等元和元素有微小扰动时的误差估计。
The main goal of this article is to show that for every (reflexive) infinite-dimensional Banach space $X$ there exists a reflexive Banach space $Y$ and $T, R \in \mathcal{L}(X,Y)$ such that $R$ is a rank-one operator, $\|T+R\|>\|T\|$ but $T+R$ does not attain its norm. This answers a question posed by S. Dantas and the first two authors. Furthermore, motivated by the parallelism exhibited in the literature between the $V$-property introduced by V.A. Khatskevich, M.I. Ostrovskii and V.S. Shulman and the weak maximizing property introduced by R.M. Aron, D. García, D. Pellegrino and E.V. Teixeira…
We study bounded actions of groups and semigroups $G$ on exact sequences of Banach spaces from the point of view of quasilinear maps, characterize the actions on the twisted sum space by commutator estimates and introduce the associated notions of $G$-centralizer and $G$-equivariant map. We will show that when (A) $G$ is an amenable group and (U) the target space is complemented in its bidual by a $G$-equivariant projection, then uniformly bounded compatible families of operators generate bounded actions on the twisted sum space; that compatible quasilinear maps are linear perturbations of $G$…
This paper generalizes results for alternate dual frames in Hilbert spaces on the situation of a Banach space. Additionally some properties of synthesys operator associated with alternate dual frame are investigated. The main result is that for a given cross-frame in Banach space we can not find such strongly continuous uniformely bounded one-parameter group of operators that the vectors from this cross-frame are eigenvectors of group's operators.
Motivated to generalize the Fourier frame concept to Banach spaces we introduce (p, q)-Bessel/frame measures for a given finite measure on LCA groups. We also present a general way of constructing (p, q)-Bessel/frame measures for a given measure. Moreover, we prove that if a measure has an associated (p, q)-frame measure, then it must have a certain uniformity in the sense that the weight is distributed quite uniformly on its support. Next, we show that if the measures $μ$ and $λ$ without atoms whose supports form a packing pair, then $μ\astλ+δ_g\astμ$ does not admit any (p, q)-frame measure. …
In this paper, a sufficient condition for the existence of hyperinvariant subspace of compact perturbations of multiplication operators on some Banach spaces is presented. An interpretation of this result for compact perturbations of normal and diagonal operators on Hilbert space is also discussed. An improvement of a result of [FX12] for compact perturbations of diagonal operators is also obtained.
It is known in Hilbert space frame theory that a Bessel sequence can be expanded to a frame. Contrary to Hilbert space situation, using a result of Casazza and Christensen, we show that there are Banach spaces and approximate Bessel sequences which can not be expanded to approximate Schauder frames. We characterize Banach spaces in which one can expand approximate Bessel sequences to approximate Schauder frames.
If T is a bounded linear operator acting on an infinite-dimensional Banach space, then there exists and operator F of rank at most one and arbitrarily small norm such that T-F has an invariant subspace of infinite dimension and codimension. This improves results of Tcaciuc and other authors.
We define the frame potential for a Schauder frame on a finite dimensional Banach space as the square of the $2$-summing norm of the frame operator. As is the case for frames for Hilbert spaces, we prove that the frame potential can be used to characterize finite unit norm tight frames (FUNTFs) for finite dimensional Banach spaces. We prove the existence of FUNTFs for a variety of spaces, and in particular that every $n$-dimensional complex Banach space with a $1$-unconditional basis has a FUNTF of $N$ vectors for every $N\geq n$. However, many interesting results on FUNTFs and sums of rank on…
Let X be a Banach Space over K=R or C, and let f:=F+C be a weakly coercive operator from X onto X, where F is a C^1-operator, and C a C^1 compact operator. Sufficient conditions are provided to assert that the perturbed operator f is a C^1-diffeomorphism. Three corollaries are given. The first one, when F is a linear homeomorphism. The second one, when F is a k-contractive perturbation of the identity. The third one, when X is a Hilbert space and F a particular linear operator. The proof of our results is based on properties of Fredholm operators, as well as on local and global inverse mapping…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。