Cyclic vectors of self-adjoint operators in Hilbert space
Hidayat M. Huseynov
给出了一类自伴算子的向量是循环向量的判别准则和充分条件。
A criterion and sufficient conditions for a vector to be a cyclic vector for a class of self-adjoint operators are obtained.
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 study finitely cyclic self-adjoint operators in a Hilbert space, i.e. self-adjoint operators that posses such a finite subset in the domain that the orbits of all its elements with respect to the operator are linearly dense in the space. One of the main goals here is to obtain the representation theorem for such operators in a form analogous to the one well-known in the cyclic self-adjoint operators case. To do this, we present here a detailed introduction to matrix measures, to the matrix measure $L^2$ spaces, and to the multiplication by scalar functions operators in such spaces. This all…
Spectral Theorem for a bounded self adjoint operator on a Bicomplex Hilbert space
本文在双复希尔伯特空间框架下，通过定义双复内积和双复值 $L^{2}[a,b]$ 空间，证明非紧有界自伴算子的谱定理。
Self-adjoint cyclically compact operators and their applications
本文研究有界可测函数环上Hilbert-Kaplansky模上的自伴循环紧算子.给出了这类算子的谱定理。我们将这一结果应用于可测函数的混合范数空间上的偏积分方程和与von Neumann代数相关的紧算子。给出了具有自伴随核的偏积分方程可解的一个条件。此外，还给出了关于I型vonNeumann代数的紧算子的一般形式.
We characterize the convex-cyclic weighted composition operators $W_{(u,ψ)}$ and their adjoints on the Fock space in terms of the derivative powers of $ ψ$ and the location of the eigenvalues of the operators on the complex plane. Such a description is also equivalent to identifying the operators or their adjoints for which their invariant closed convex sets are all invariant subspaces. We further show that the space supports no supercyclic weighted composition operators with respect to the pointwise convergence topology and hence with the weak and strong topologies and answers a question rais…
Various form closures associated with a fixed non-semibounded self-adjoint operator
本文研究了非半有界自伴算子形式闭包的非唯一性，建立了闭对称形式与Krein空间算子的一一对应，并指出闭对称形式可能比自伴算子携带更多信息。
On $C$-Symmetric and $C$-Self-adjoint Unbounded Operators on Hilbert Space
本文研究希尔伯特空间上关于共轭$C$的$C$-对称与$C$-自伴无界算子，给出了$C$-自伴扩张的完全描述、基于拟解析向量的判据及极分解刻画。
Locally adjointable operators on Hilbert $C^*$-modules
本文研究 Hilbert $C^*$-模间的局部可伴随算子，并在重要情形下给出其显式描述。
The parallel sum for adjoinable operators on Hilbert $C^*$-modules is introduced and studied. Some results known for matrices and bounded linear operators on Hilbert spaces are generalized to the case of adjointable operators on Hilbert $C^*$-modules. It is shown that there exist a Hilbert $C^*$-module $H$ and two positive operators $A, B\in\mathcal{L}(H)$ such that the operator equation $A^{1/2}=(A+B)^{1/2}X, X\in \cal{L}(H)$ has no solution, where $\mathcal{L}(H)$ denotes the set of all adjointable operators on $H$.
In general, it is a non trivial task to determine the adjoint $S^*$ of an unbounded operator $S$ acting between two Hilbert spaces. We provide necessary and sufficient conditions for a given operator $T$ to be identical with $S^*$. In our considerations, a central role is played by the operator matrix $M_{S,T}=\left(\begin{array}{cc} I & -T\\ S & I\end{array}\right)$. Our approach has several consequences such as characterizations of closed, normal, skew- and selfadjoint, unitary and orthogonal projection operators in real or complex Hilbert spaces. We also give a self-contained proof of the f…
Adjoint of sums and products of operators in Hilbert spaces
给出了保证希尔伯特空间之间的稠密无界算子$A,B$的方程$(A+B)^*=A^*+B^*$和$(AB)^*=B^*A^*$成立的充分必要条件.我们还改进了自伴算子和本质自伴算子的扰动理论，这是由于Nelson，Kato，Rellich和Wüst的结果。我们的方法涉及的范围内的2 × 2矩阵的形式$M_{S,T}=\left(\begin{array}{cc}\!\! I & -T\!\!\\ \!\! S& I\!\!\end{array}\right)$，使它能够处理真正的和复杂的希尔伯特空间联合。
Spectral Theorem for Self-Adjoint Partial Integral Operators in Kaplansky-Hilbert Modules
本文在Kaplansky-希尔伯特模块中证明了自伴偏积分算子的谱定理，推广了Mercer定理并给出了具体例子。
Commutators of the Unilateral Shift and Adjoint for Reproducing Kernel Hilbert Spaces on the Disk
该文将Berger-Shaw迹公式从Hardy空间推广至单位圆盘上更广的旋转不变再生核希尔伯特空间，并给出内积实例及加权移位扩展。
In this article, we completely characterize the complex symmetry, cyclicity and hypercyclicity of composition operators $C_ϕf=f\circϕ$ induced by affine self-maps $ϕ$ of the right half-plane $\mathbb{C}_+$ on the Hardy-Hilbert space $H^2(\mathbb{C}_+)$. We also provide new proofs for the normal, self-adjoint and unitary cases and for an adjoint formula discovered by Gallardo-Gutiérrez and Montes-Rodrígues.
A non standard approach of spectral theory of self-adjoint operators (generalized Gelfand eigenvectors)
设$u=\int_{-\infty}^{+\infty}λdE_λ$是希尔伯特空间$H$中的自伴算子.我们的目的是提供一个非标准的描述谱族$(E_λ)$和广义Gelfand特征向量。
We construct self-adjoint operators in the direct sum of a complex Hilbert space $H$ and a finite dimensional complex inner product space $W$. The operator theory developed in this paper for the Hilbert space $H\oplus W$ is originally motivated by some fourth-order differential operators, studied by Everitt and others, having orthogonal polynomial eigenfunctions. Generated by a closed symmetric operator $T_{0}$ in $H$ with equal and finite deficiency indices and its adjoint $T_{1}$, we define \textit{families} of minimal operators $\{\widehat{T}_{0}\}$ and maximal operators $\{\widehat{T}_{1}\…
The spectrum of the Hilbert space valued second derivative with general self-adjoint boundary conditions
本文考虑了向量值函数空间上一类与二阶导数有关的自伴椭圆问题。我们提出了两种不同的方法来研究相关的特征值问题。第一个，更一般的一个允许取代世俗方程（这是众所周知的，在某些特殊情况下）由一个抽象的排名条件。后者似乎特别适用于一个特定的边界条件，有时被称为“反基尔霍夫”在文献中，出现在理论的微分算子的图形;它也允许讨论有趣的和更直接的连接之间的频谱的微分算子和一些图论数量。在任何一种情况下，我们的结果产生，除其他外，一些结果的对称性的频谱。
Let $n$ be any natural number. The $n$-centered operator is introduced for adjointable operators on Hilbert $C^*$-modules. Based on the characterizations of the polar decomposition for the product of two adjointable operators, $n$-centered operators, centered operators as well as binormal operators are clarified, and some results known for the Hilbert space operators are improved. It is proved that for an adjointable operator $T$, if $T$ is Moore-Penrose invertible and is $n$-centered, then its Moore-Penrose inverse is also $n$-centered. A Hilbert space operator $T$ is constructed such that $T…
Spectral theorem for compact self-adjoint operators on smooth Banach spaces
该研究针对光滑巴拿赫空间上关于对偶映射自伴的紧算子，建立了谱表示定理，是希尔伯特空间相关经典谱定理的自然类似物。
Cyclic frames in finite-dimensional Hilbert spaces
本文推广Kalra的定义，分析有限维希尔伯特空间中的循环框架（动态框架子类），通过替代方法提供动态框架刻画并推导出循环框架刻画，为擦除问题相关框架研究提供新视角。
Spectral theory of discontinuous functions of self-adjoint operators: essential spectrum
设$H_0$和$H$是希尔伯特空间中的自伴算子.在散射理论的框架下，我们描述了分段连续函数$φ$的差分$φ(H)-φ(H_0)$的本质谱。该描述涉及$H$、$H_0$对的散射矩阵。
Some inequalities for adjointable operators on Hilbert $C^*$-modules
本文在 Hilbert $C^*$-模的可伴随算子框架下研究正性与不等式，建立无条件的 $2\ imes2$ 分块矩阵正性判据及带参数的推广混合 Schwarz 不等式。
In this paper we solve the problem of approximating functionals $(φ(A)x, f)$ (where $φ(A)$ is some function of self-adjoint operator $A$) on the class of elements of a Hilbert space that is defined with the help of another function $ψ(A)$ of the operator $A$. In addition, we obtain a series of sharp Taikov-type additive inequalities that estimate $|(φ(A)x, f)|$ with the help of $\| ψ(A)x\|$ and $\| x\|$. We also present several applications of the obtained results. First, we find sharp constants in inequalities of the type used in H${\rm{\ddot{o}}}$rmander theorem on comparison of operators in…
A bounded linear Hilbert space operator $S$ is said to be a $2$-isometry if the operator $S$ and its adjoint $S^*$ satisfy the relation $S^{*2}S^{2} - 2 S^{*}S + I = 0$. In this paper, we study Hilbert space operators having liftings or dilations to $2$-isometries. The adjoint of an operator which admits such liftings is characterized as the restriction of a backward shift on a Hilbert space of vector-valued analytic functions. These results are applied to concave operators (i.e., operators $S$ such that $S^{*2}S^{2} - 2 S^{*}S + I \le 0$) and to operators similar to contractions or isometries…
On chaoticity of the sum of chaotic shifts with their adjoints in Hilbert space and applications to some chaotic weighted shifts acting on some Fock-Bargmann spaces
本文概述了作者近年来对作用于某些Fock-Bargmann空间上的具体的bakward无界移位算子的混沌性所做的一些工作，并给出了作用于希尔伯特空间上的线性无界稠定混沌移位算子$T$是混沌的充分条件，其中$T^*$是它的伴随算子.
Cyclic Hilbert spaces and Connes' embedding problem
设$M$是一个具有迹$τ$的$II_1$ -因子，$L^2(M,τ)$的线性子空间不仅是普通的希尔伯特空间，而且具有附加结构.我们引入循环线性空间的概念，把这些性质作为公理。在第二节中，我们提出了以下问题：“对于某些$M$，是否每个循环希尔伯特空间都嵌入到$L^2(M,τ)$中？".肯定的回答意味着存在一种算法来检验Connes的嵌入猜想。在第3节中，我们为回答上一个问题迈出了第一步。
On adjoint invariant classes of shift operators
本文研究 Hilbert 空间上加权广义移位算子的伴随不变性，证明由共轭不变子集生成的加法半群伴随不变当且仅当空间有限维或 0 不是该子集的极限点。
Maps on real Hilbert spaces preserving the area of parallelograms and a preserver problem on self-adjoint operators
本文首先用$2\leq d<\infty$描述了$\mathbb{R}^d$上的所有（不一定是线性或双射）变换，这些变换保持了任意两个向量所张成的平行四边形的面积。我们还刻画了任意实希尔伯特空间上保持后一个量的双射（不一定是线性的）。这回答了Rassias和Wagner提出的一个问题，它可以被认为是著名的实希尔伯特空间上的Wigner定理的一个变体，该定理在量子力学中起着重要作用。因此，我们解决了Molnár和Timmermann的一个问题，该问题仅在二维情况下顽固地保持开放。最后，这个二维的结果将被应用，以加强他们的定理在更高的维度。
Generalized Polar Decompositions for Closed Operators in Hilbert Spaces and Some Applications
研究了希尔伯特空间中稠密闭线性算子的广义极式分解，并给出了自伴、正规和m-扇形算子的相对（形式）有界和相对（形式）紧扰动的一些应用.
In this paper, we will generelize $b$-frames; a new concept of frames for Hilbert spaces, by $K$-$b$-frames. The idea is to take a sequence from a Banach space and see how it can be a frame for a Hilbert space. Instead of the scalar product we will use a new product called the $b$-dual product and it is constructed via a bilinear mapping. We will introduce new results about this product, about $b$-frames, and about $K$-$b$-frames, and we will also give some examples of both $b$-frames and $K$-$b$-frames that have never been given before. We will give the expression of the reconstruction formul…
On convex-cyclic operators
给出了凸循环性的一个Hahn-Banach刻画。我们还得到了Banach空间上有界线性算子$S$的一个例子，其中$σ_{p}(S^*)=\emptyset$使得$S$是凸循环的，但$S$不是弱超循环的，并且$S^2 $不是凸循环的.这解决了$σ_p(S^*)=\varnothing$在\cite{Rezaei}中Rezaei的两个问题。最近，León-Saavedra和Romero de la Rosa \cite{LeRo}提供了一个凸循环算子$S$的例子，使得幂$S^n$与$σ_p(S^*)\neq \varnothing$不能是凸循环的。事实上，他们解决了树的问题所提出的Rezaei在\cite{Rezaei}。证明了$m$ -等距不是凸循环的，而$\varepsilon$ -超循环算子是凸循环的.我们还刻画了可对角化的凸循环正规算子，并给出了任意算子的特征值是凸循环的条件。我们证明了某些伴随乘法算子是凸循环的，并证明了某些算子是凸循环的，但没有一个算子的凸多项式是超循环的。另外，一些伴随乘法算子是凸循环的，但不是1-弱超循环的。
It is proved that for adjointable operators $A$ and $B$ between Hilbert $C^*$-modules, certain majorization conditions are always equivalent without any assumptions on $\overline{\mathcal{R}(A^*)}$, where $A^*$ denotes the adjoint operator of $A$ and $\overline{\mathcal{R}(A^*)}$ is the norm closure of the range of $A^*$. In the case that $\overline{{\mathcal R}(A^*)}$ is not orthogonally complemented, it is proved that there always exists an adjointable operator $B$ whose range is contained in that of $A$, whereas the associated equation $AX=B$ for adjointable operators is unsolvable.
A Hilbert space operator $A\in\B$ is left $(X,m)$-invertible by $B\in\B$ (resp., $B\in\B$ is an $(X,m)$-adjoint of $A\in\B$) for some operator $X\in\B$ if $\triangle_{B,A}^m(X)=\sum_{j=0}^m(-1)^j\left(\begin{array}{clcr}m\\j\end{array}\right)B^{m-j}XA^{m-j}=0$ (resp., $δ_{B,A}^m(X)=\sum_{j=0}^m(-1)^j\left(\begin{array}{clcr}m\\j\end{array}\right)B^{(m-j)}XA^j=0$). No Drazin invertible operator $A\in\B$, with Drazin inverse $A_d$, can be left $(I,m)$-invertible (equivalently, $m$-invertible) by its adjoint or its Drazin inverse or the adjoint of its Drazin inverse. For Drazin inverrtible operat…
Normality of adjointable module maps
讨论了有界和无界伴随算子的正规性。设$T$是Hilbert C*-模之间的一个具有极式分解的伴随算子，则$T$是正规的当且仅当存在一个酉算子$ \mathcal{U}$与$T$和$T^*$交换，使得$T=\mathcal{U} \, T^*.$ Kaplansky关于有界算子乘积的正规性定理也在Hilbert C*-模的框架下得到了重新表述.
On multipliers of Hilbert modules over locally C*-algebras
本文研究了局部C* 代数上Hilbert模的乘子模的结构以及从Hilbert A-模E到Hilbert A-模F的所有可伴随算子的集合与从E的乘子模M（E）到F的乘子模M（F）的所有可伴随算子的集合之间的关系.
Partially fundamentally reducible operators in Krein spaces
Krein空间$\bigl({\mathcal K},[\,\cdot\,,\cdot\,]\bigr)$中的自伴算子$A$称为部分基本可约的，如果存在基本分解${\mathcal K} = {\mathcal K}_+ [\dot{+}] {\mathcal K}_-$（其不约化$A$）和分别在希尔伯特空间$\bigl({\mathcal K}_+,[\,\cdot\,,\cdot\,]\bigr)$和$\bigl({\mathcal K}_-,-[\,\cdot\,,\cdot\,]\bigr)$中密集定义的对称算子$S_+$和$S_-$，使得每个$S_+$和$S_-$具有缺陷号$(1,1)$，并且操作符$A$是自Krein空间$\bigl({\mathcal K},[\,\cdot\,,\cdot\,]\bigr)$中$S =S_+ \oplus (-S_-)$的伴随扩张。算子$A$被解释为算子$S_+$和$-S_-$相对于某些边界三元组$\bigl({\mathbb C},Γ_0^+,Γ_1^+\bigr)$和$\bigl({\mathbb C},Γ_0^-,Γ_1^-\bigr)$的耦合。利用$S_+$和$S_-$相对于边界三元组$\bigl({\mathbb C},Γ_0^+,Γ_1^+\bigr)$和$\bigl({\mathbb C},Γ_0^-,Γ_1^-\big…
On the binary relation $\leq_u$ on self-adjoint Hilbert space operators
给定自伴算子$A, B\in\mathbb{B}(\mathscr{H})$，则称$A\leq_uB$，只要$A\leq U^*BU$对于某个酉算子$U$。证明了$A\leq_u B$的充要条件是对任意增算子凸函数$f$，任意算子单调函数$g$和任意正数$r$，都有$f(g(A)^r)\leq_uf(g(B)^r)$.我们给出了一些充分条件，在此条件下，如果$B\leq A\leq U^*BU$，则$B=A=U^*BU$。最后证明了如果$A^n\leq U^\ast A^nU$对所有$n\in\mathbb{N}$，则$A=U^\ast AU$ .
Self-adjoint extensions with compact resolvent
本文研究了在可分复Hilbert空间中，闭对称算子具有紧谱的自共轭扩展的充要条件，并给出了其参数化方法。
Characterization of Frame-Related Sequences on Semi-Hilbert Spaces
本文针对半希尔伯特空间，研究稠定可闭算子的约化加权伴随，构造框架型系统并刻画AB-贝塞尔序列、AB-框架等，导出AB-框架的道格拉斯型值域刻画。
Finite rank perturbations and solutions to the operator Riccati equation
考虑复可分希尔伯特空间$\mathfrak{H}_0 \oplus \mathfrak{H}_1$中自伴算子的非对角自伴有限秩扰动，其中$\mathfrak{H}_1$是有限维的.我们描述的奇异谱的扰动算子，并建立一个连接与解决方案的运营商Riccati方程。特别地，我们证明了在整个希尔伯特空间是有限维的情况下解的存在性结果。
Non-self-adjoint harmonic oscillator, compact semigroups and pseudospectra
我们提供了有关复谐振子赝谱的新信息。我们的分析说明了两种不同的技术得到预解范数估计。第一种方法采用JWKB方法，并推广了E.B.戴维斯第二个依赖于复谐振子生成的有界全纯半群在极大角域上是Hilbert-Schmidt型的。为了证明这最后一个性质，我们推导出经典Mehler公式的非自伴形式。
In a previous paper, the authors introduced the idea of a symmetric pair of operators as a way to compute self-adjoint extensions of symmetric operators. In brief, a symmetric pair consists of two densely defined linear operators $A$ and $B$, with $A \subseteq B^\star$ and $B \subseteq A^\star$. In this paper, we will show by example that symmetric pairs may be used to deduce closability of operators and sometimes even compute adjoints. In particular, we prove that the Malliavin derivative and Skorokhod integral of stochastic calculus are closable, and the closures are mutually adjoint. We als…
A note on Jensen inequality for self-adjoint operators
本文考虑一类希尔伯特空间上的自伴算子的类序关系。利用Jensen不等式定义了这个关系。我们将证明，在某些假设下，这个关系是反对称的。
Self-Adjoint Extension of Symmetric Maps
从实希尔伯特空间到实希尔伯特空间的稠密定义对称线性映射扩张到自伴映射。扩展通过Riesz表示来表示。对于强单调映射的Friedrichs扩张，自伴扩张是唯一的，并且等于给定映射的闭包。
Cyclicity in rank-one perturbation problems
线性算子的循环性，或者等价地说它的谱的简单性，是一个重要的谱特征，它出现在泛函分析的许多问题和数学物理的应用中。在本文中，我们研究自伴和酉算子秩一扰动问题的循环性。我们表明，对于一个固定的非零向量的属性是一个循环向量并不罕见，在这个意义上说，对于任何家庭的秩一扰动的自伴或酉算子作用于空间，该向量将是循环的家庭的每个运营商，与一个可能的例外的一个小的设置相对于参数。我们讨论了应用我们的结果安德森型哈密顿。
Automatic Boundedness of Adjointable Operators on Barreled VH-Spaces
本文证明了在巴雷尔VH空间上，可调算子自动有界，并探讨了其在VH空间扩张理论中的应用。
The generalized polar decomposition, the weak complementarity and the parallel sum for adjointable operators on Hilbert $C^*$-modules
本文研究 Hilbert $C^*$-模上伴随算子，引入广义极分解工具建立弱可补算子理论，并证明了相关算子方程解的唯一性、可补性反例及平行和方程的可解性。
On properties of normal operators and self-adjoint operators on smooth Banach spaces
本文探讨光滑巴拿赫空间上正规和幺正算子的性质，扩展了从希尔伯特空间到巴拿赫空间的经典概念，并研究自伴随算子的范数、最小模、数值半径等性质及谱特性。
In a real Hilbert spaces H a smooth operator F is studied, whose derivative at each point of its domain is a symmetric operator. In terms of abstract boundary conditions locally self-adjoint extensions of this operator are described. We use some concepts and facts from symplectic differential geometry.
Complementary Lagrangians in Infinite Dimensional Symplectic Hilbert Spaces
利用无界自伴算子的谱定理，证明了辛希尔伯特空间的任意可数拉格朗日子空间族都存在一个公共的互补拉格朗日量.
Functional Calculus for definitizable self-adjoint linear relations on Krein spaces
本文发展了Krein空间上自伴可定义线性关系的谓词演算$ϕ\mapsto ϕ(A)$.这个谓词演算是希尔伯特空间情形中的$ϕ\mapsto \int ϕ\, dE$的适当模拟。它还包括频谱定理的自伴可定义运营商的克莱因空间显示存在的频谱投影。
Lower bounds for self-adjoint Sturm-Liouville operators
本研究针对加权L²希尔伯特空间中三系数Sturm-Liouville微分表达式对应的自伴算子，给出其下界的估计结果。
A row and a column of two linear relations in Hilbert spaces are presented respectively as a sum and an intersection of two linear relations. As an application, necessary and sufficient conditions for the adjoint of a column to be a row are examined. Several outcomes are discussed as well.
Non-self-adjoint resolutions of the identity and associated operators
研究了Hilbert空间中由恒等式$\{X(λ)\}_{λ\in {\mb R}}$的非自伴分解定义的闭算子，其伴随也构成恒等式的分解.特别地，证明了闭算子$B$具有与自伴算子相似的谱表示当且仅当$B=TAT^{-1}$，其中$A$是自伴算子，$T$是具有有界逆的有界算子.
On extensions of $J$-skew-symmetric and $J$-isometric operators
本文证明了Hilbert空间$H$中的每个稠定$J$ -反对称算子（或每个具有$\overline{D(A)}=\overline{R(A)}=H$的$J$ -等距算子）在Hilbert空间$\widetilde H\supseteq H$中有$J$ -反自伴（或$J$ -酉）扩张.我们遵循Galindo在~[A.~]中的思想。Galindo，关于$J$的存在性-$J$的自伴扩展-具有伴随的对称算子，《纯粹数学和应用数学通讯》，第十五卷，423-425（1962）]，并进行了必要的修改。
Notes on the numerical radius for adjointable operators on Hilbert $C^*$-modules
本文研究 Hilbert $C^*$-模上可共轭算子的数值半径，证明正规算子满足 $w(T)=\\|T\\|$，构造反例说明一般情形不成立，并给出空间数值半径的新刻画及忠实表示下的不等式。
We provide necessary and sufficient conditions for a pair $S,T$ of Hilbert space operators in order that they satisfy $S^*=T$ and $T^*=S$. As a main result we establish an improvement of von Neumann's classical theorem on the positive self-adjointness of $S^*S$ for two variables. We also give some new characterizations of self-adjointness and skew-adjointness of operators, not requiring their symmetry or skew-symmetry, respectively.
Complex-self-adjointness
本文提出希尔伯特空间中经非自逆反酉算子与伴随算子相似的算子概念，研究其延拓理论、极分解和反线性本征函数展开，以刻画量子力学中非自伴算子的物理对称性。
We propose a new approach to construct the eigenvalue expansion in a weighted Hilbert space of the solution to the Cauchy problem associated to Gauss-Laguerre invariant Markov semigroups that we introduce. Their generators turn out to be natural non-self-adjoint and non-local generalizations of the Laguerre differential operator. Our methods rely on intertwining relations that we establish between these semigroups and the classical Laguerre semigroup and combine with techniques based on non-harmonic analysis. As a by-product we also provide regularity properties for the semigroups as well as f…
On almost commuting matrices with respect to the normalized Hilbert--Schmidt norm
本文针对归一化希尔伯特-施密特范数下的几乎可交换矩阵Rosenthal–Halmos问题，给出了自伴矩阵逼近的误差估计，证明了指数1/3无法改进。
A note on the Jensen inequality for self-adjoint operators. II
这是我们上一篇论文的延续。考虑了希尔伯特空间上正算子的某种类序关系。这个关系是通过使用关于平方根函数的Jensen不等式定义的。我们表明，这种关系是反对称的，如果运营商是可逆的。
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。