Beata Randrianantoanina
We characterize norm one complemented subspaces of Orlicz sequence spaces $\ell_M$ equipped with either Luxemburg or Orlicz norm, provided that the Orlicz function $M$ is sufficiently smooth and sufficiently different from the square function. This paper concentrates on the more difficult real case, the complex case follows from previously known results.
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We prove that there is no 1-complemented subspace of finite codimension in separable rearrangament-invariant function spaces.
In this paper, we firstly character the structures of symmetries $J$ such that a projection $P$ is $J$-contractive. Then the minimal and maximal elements of the symmetries $J$ with $P^{\ast}JP\leqslant J$(or $JP\geqslant0)$ are given. Moreover, some formulas between $P_{(2I-P-P^{\ast})^{+}}$ $(P_{(2I-P-P^{\ast})^{-}})$ and $P_{(P+P^{\ast})^-}$ $(P_{(P+P^{\ast})^+})$ are established.
We characterize 1-complemented subspaces of finite codimension in strictly monotone one-$p$-convex, $2<p<\infty,$ sequence spaces. Next we describe, up to isometric isomorphism, all possible types of 1-unconditional structures in sequence spaces with few surjective isometries. We also give a new example of a class of real sequence spaces with few surjective isometries.
Extension of contractive projections
本文通过建立扩张定理，给出了Hardy空间中所有收缩投影和1-补子空间的显式表达式，并证明了其非平凡1-补子空间的等距同构性质，回答了Wojtaszczyk在2003年提出的问题。
Contractive projections, conditional expectations, and idempotent coefficient multipliers on $H^p$ spaces $(0<p<1)$
本文研究了 $0<p<1$ 时 Hardy 空间上的压缩投影、条件期望与幂等系数乘子，通过建立概率 $L^p$ 空间中压缩投影的延拓定理，完整刻画了 $d$ 维环面上此类乘子，补充了现有结果。
Given a JBW*-triple Z and a normal contractive projection P on Z, we show that the (Murray-von Neumann) type of each summand of P(Z) is dominated by the type of Z.
The author established the affine Orlicz Polya-Szego principle for log-concave functions and conjectured that the principle can be extended to the general Orlicz Sobolev functions. In this paper, we confirm this conjecture completely. An affine Orlicz Polya-Szego principle, which includes all the previous affine Polya-Szego principles as special cases, is formulated and proved. As a consequence, an Orlicz-Petty projection inequality for star bodies is established.
We constructed a unitary semigroup $(e^{tA})_{t \geq 0}$ on a Hilbert space and an orthogonal projection $P$ such that the limit $\lim_{n \to \infty} [ e^{\frac{t}{n}A}P ]^n$ does not exist strongly. A similar example with a positive contractive semigroup and positive contractive projection on $L_p$ is also constructed.
Let $S_1$ and $S_2$ be disjoint finite unions of parallelepipeds. We describe necessary and sufficient conditions on the sets $S_1,S_2$ and exponents $p$ such that the canonical projection $P$ from $PW_{S_1\cup S_2}^p$ to $PW_{S_1}^p$ is a contraction.
We prove a conjecture of Wojtaszczyk that for $1\leq p<\infty$, $p\neq 2$, $H_p(\mathbbT)$ does not admit any norm one projections with dimension of the range finite and bigger than 1. This implies in particular that for $1\leq p<\infty$, $p\ne 2$, $H_p$ does not admit a Schauder basis with constant one.
On the structure of contractively decomposable projections on noncommutative $L^p$-spaces and Schatten spaces
【一句话总结】研究 \(1 < p < \infty\) 时非交换Haagerup \(L^p\) 空间上压缩可分解投影范围的同构情况，在Schatten空间有更精确描述，还证明了Schatten空间上压缩1 - 伪可分解投影与压缩可分解投影的等价性。
Positive contractive projections on noncommutative $\mathrm{L}^p$-spaces and nonassociative $\mathrm{L}^p$-spaces
本文改进了已有研究，精确刻画了与 $σ$-有限冯·诺依曼代数相关的非交换 $\mathrm{L}^p$ 空间上的正压缩投影，并证明其值域在多数情况下与 $\mathrm{JW}^*$-代数相关的非结合 $\mathrm{L}^p$ 空间等距。
We consider 1-complemented subspaces (ranges of contractive projections) of vector-valued spaces $\ell_p(X)$, where $X$ is a Banach space with a 1-unconditional basis and $p \in (1,2)\cup (2,\infty)$. If the norm of $X$ is twice continuously differentiable and satisfies certain conditions connecting the norm and the notion of disjointness with respect to the basis, then we prove that every 1-complemented subspace of $\ell_p(X)$ admits a basis of mutually disjoint elements. Moreover, we show that every contractive projection is then an averaging operator. We apply our results to the space $\ell…
A modular theory of contractive projections on Banach spaces with applications to noncommutative $\mathrm{L}^p$-spaces
本文提出基于 Levi 形式的模理论，刻画 Banach 空间压缩投影，并应用于非交换 L^p 空间，证明 2-压缩投影等价于完全压缩，且值域具有三元结构。
Completely isometric subspaces of noncommutative $\mathrm{L}^p$-spaces and contractive projections
该研究针对1<p<∞且p≠2的非交换L^p空间，建立正压缩投影值域完全等距于另一非交换L^p空间时必为完全正投影的结论，还刻画了可压缩分解投影的值域特征。
We study contractive projections, isometries, and real positive maps on algebras of operators on a Hilbert space. For example we find generalizations and variants of certain classical results on contractive projections on C*-algebras and JB-algebras due to Choi, Effros, Størmer, Friedman and Russo, and others. In fact most of our arguments generalize to contractive `real positive' projections on Jordan operator algebras, that is on a norm-closed space A of operators on a Hilbert space which are closedunder the Jordan product. We also prove many new general results on real positive maps which a…
Parallel to the study of finite dimensional Banach spaces, there is a growing interest in the corresponding local theory of operator spaces. We define a family of Hilbertian operator spaces H_n^k,0< k < n+1, generalizing the row and column Hilbert spaces R_n,C_n and show that an atomic subspace X of B(H) which is the range of a contractive projection on B(H) is isometrically completely contractive to a direct sum of the H_n^k and Cartan factors of types 1 to 4. In particular, for finite dimensional X, this answers a question posed by Oikhberg and Rosenthal. Explicit in the proof is a classific…
Let X be an L_1-predual space and let K be a countable linearly independent subset of the extreme points of its closed dual ball. It is shown that if the norm-closed linear span Y of K is w^*-closed in X^*, then Y is the range of a w^*-continuous contractive projection in X^*. This result is applied in order to provide new and simpler proofs of the results of Lazar, Lindenstrauss and Zippin on the embedding of C(K) spaces into X.
In 1965, Ron Douglas proved that if $X$ is a closed subspace of an $L^1$-space and $X$ is isometric to another $L^1$-space, then $X$ is the range of a contractive projection on the containing $L^1$-space. In 1977 Arazy-Friedman showed that if a subspace $X$ of $C_1$ is isometric to another $C_1$-space (possibly finite dimensional), then there is a contractive projection of $C_1$ onto $X$. In 1993 Kirchberg proved that if a subspace $X$ of the predual of a von Neumann algebra $M$ is isometric to the predual of another von Neumann algebra, then there is a contractive projection of the predual of…
2-positive contractive projections on noncommutative $\mathrm{L}^p$-spaces
本文研究非交换L^p空间上的2-正压缩投影问题，证明其值域完全等距序同构于某个非交换L^p空间，该结果对Schatten空间亦为全新结论，方法上本质依赖非迹的Haagerup非交换L^p空间。
Positive contractive projections in Schatten Spaces
本文研究了Schatten空间中正1-补足子空间的特征，基于Arazy和Friedman的工作，确定了五种互不相同的不可分解正1-补足子空间类型，并证明所有正1-补足子空间均可表示为这些不可分解子空间的直和。
The main goal of this paper is to find operator algebra variants of certain deep results of Stormer, Friedman and Russo, Choi and Effros, Effros and Stormer, Robertson and Youngson, Youngson, and others, concerning projections on C*-algebras and their ranges. (See papers of these authors referenced in the bibliography.) In particular we investigate the `bicontractive projection problem' and related questions in the category of operator algebras. To do this, we will add the ingredient of `real positivity' from recent papers of the first author with Read.
Let $d\in\mathbb N$ and $f$ be a function in the Orlicz class $L(\log^+L)^{d-1}$ defined on the unit cube $[0,1]^d$ in $\mathbb{R}^d$. Given partitions $Δ_1,\ldots,$ $Δ_d$ of $[0,1]$, we first prove that the orthogonal projection $P_{(Δ_1,\dots,Δ_d)}(f)$ onto the space of tensor product splines with arbitrary orders $(k_1,\dots, k_d)$ and knots $Δ_1,\ldots,Δ_d$ converges to $f$ almost everywhere as the mesh diameters $|Δ_1|,\ldots, |Δ_{d}|$ tend to zero. This extends the one-dimensional result in [Passenbrunner and Shadrin, Journal of Approximation Theory, 2014] to arbitrary dimensions. In a s…
Contractive inequalities between Dirichlet and Hardy spaces
本文证明了 Brevig 等人关于 Dirichlet 空间与 Hardy 空间之间压缩不等式的猜想，并探讨了其与 Riesz 投影的联系。
We state and discuss several interrelated results, conjectures, and questions regarding contractive inequalities for classical $H^p$ spaces of the unit disc. We study both coefficient estimates in terms of weighted $\ell^2$ sums and the Riesz projection viewed as a map from $L^q$ to $H^p$ with $q\ge p$. Some numerical evidence is given that supports our conjectures.
Schauder-Orlicz decompositions, $\ell_Φ$-decompositions and pseudo-Daugavet property
本文推广了Banach空间的$\ell_p$-分解概念，提出$\ell_Φ$-分解与Schauder-Orlicz分解，并证明在具有伪Daugavet性质的空间中不存在包含有限维子空间的此类分解。
On the contractivity of the Riesz projection
本文证明了Riesz投影在$1<q<\infty$时从$L^q$到$L^{4(1-1/q)}$的压缩性，填补了相关猜想未解决的参数范围。
We construct some separable infinite dimensional homogeneous Hilbertian operator spaces which generalize the row and column spaces R and C. We show that separable infinite-dimensional Hilbertian JC*-triples are completely isometric to an element of the set of (infinite) intersections of these spaces. This set includes the operator spaces R, C, their intersection, and the space spanned by creation operators on the full anti-symmetric Fock space. In fact, we show that these new spaces are completely isometric to the space of creation (resp. annihilation) operators on the anti-symmetric tensors o…
We prove that if $X$ is a complex strictly monotone sequence space with $1$-unconditional basis, $Y \subseteq X$ has no bands isometric to $\ell_2^2$ and $Y$ is the range of norm-one projection from $X$, then $Y$ is a closed linear span a family of mutually disjoint vectors in $X$. We completely characterize $1$-complemented subspaces and norm-one projections in complex spaces $\ell_p(\ell_q)$ for $1 \leq p, q < \infty$. Finally we give a full description of the subspaces that are spanned by a family of disjointly supported vectors and which are $1$-complemented in (real or complex) Orlicz or …
A basic result in semigroup theory states that every $C_0$-semigroup is quasi-contractive with respect to some appropriately chosen equivalent norm. This paper contains a counterpart of this well-known fact. Namely, by examining the convergence of the Trotter-type formula $(e^{\frac{t}{n}A}P)^n$ (where $P$ denotes a bounded projection), we prove that whenever the generator $A$ is unbounded it is possible to introduce an equivalent norm on the space with respect to which the semigroup is {\it{not}} quasi-contractive.
In [A dozen de {F}inetti-style results in search of a theory, Ann. Inst. H. Poincaré Probab. Statist. 23(2)(1987), 397--423], Diaconis and Freedman studied low-dimensional projections of random vectors from the Euclidean unit sphere and the simplex in high dimensions, noting that the individual coordinates of these random vectors look like Gaussian and exponential random variables respectively. In subsequent works, Rachev and Rüschendorf and Naor and Romik unified these results by establishing a connection between $\ell_p^N$ balls and a $p$-generalized Gaussian distribution. In this paper, we …
Some results on fixed points related to the contractive compositions of bounded operators in complete metric spaces are discussed through the manuscript. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators.
Generalized tri-circular projections on some spaces of analytic functions
本文研究开单位圆盘上Hardy、Bergman、Bloch等Banach函数空间及$\u27e8K\u27e9$值解析函数空间$S^p_{\mathcal{K}}$上的广义三圆压缩投影，给出其结构与完整刻画，丰富了解析函数空间的投影理论。
We introduce a noncommutative analogue of the absolute value of a regular operator acting on a noncommutative $\mathrm{L}^p$-space. We equally prove that two classical operator norms, the regular norm and the decomposable norm are identical. We also describe precisely the regular norm of several classes of regular multipliers. This includes Schur multipliers and Fourier multipliers on some unimodular locally compact groups which can be approximated by discrete groups in various senses. A main ingredient is to show the existence of a bounded projection from the space of completely bounded $\mat…
Transfinite Iteration of Operator Transforms and Spectral Projections in Hilbert and Banach Spaces
研究了有界算子变换多层迭代的收敛性，在泛函演算假设下证明了向谱投影的强收敛，并提供了显式滤波器、单调性界及反例。
Consider the projection of an $n$-dimensional random vector onto a random $k_n$-dimensional basis, $k_n \leq n$, drawn uniformly from the Haar measure on the Stiefel manifold of orthonormal $k_n$-frames in $\mathbb{R}^n$, in three different asymptotic regimes as $n \rightarrow \infty$: "constant" ($k_n=k$), "sublinear" ($k_n \rightarrow \infty$ but $k_n/n \rightarrow 0$) and "linear" $k_n/n \rightarrow λ$ with $0 < λ\le 1$). When the sequence of random vectors satisfies a certain "asymptotic thin shell condition", we establish annealed large deviation principles (LDPs) for the corresponding se…
Semiprojective Banach lattices
研究半射性巴拿赫格局的性质，证明Banach格C(X)半射性当且仅当X是绝对邻域拉回，且展示无限可数的ℓ₁和的1+项目性巴拿赫格局为半射性但不一定是1+项目性，同时证明ℓ_p和L_p空间不满足半射性。
Monomial bases for holomorphic functions on Banach spaces with an unconditional basis
本文针对具有无条件基的复巴拿赫空间，证明特定排序的单项式构成其带紧开拓扑的整全纯函数空间的Schauder基，并将结果应用于多类巴拿赫序列格与向量值E-和空间。
Let $Ω_+$ be either the open unit disc or the open upper half plane or the open right half plane. In this paper, we compute the norm of the basic operator $A_α=Π_ΘT_{b_α}|_{\mathcal{H}(Θ)}$ in the vector valued model space $\mathcal{H}(Θ)=H^m_2 \ominus ΘH^m_2$ associated with an $m\times m$ matrix valued inner function $Θ$ in $Ω_+$ and show that the norm is attained. Here $Π_Θ$ denotes the orthogonal projection from the Lebesgue space $L^m_2$ onto $\mathcal{H}(Θ)$ and $T_{b_α}$ is the operator of multiplication by the elementary Blaschke factor $b_α$ of degree one with a zero at a point $α\in …
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