Ideals in the Roe Algebras of Discrete Metric Spaces with Coefficients in B（H）

The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu＇s property A, the ideal structure of the Roe algebra of X with coefficients in B（H） is completely characterized by the ideal families of weighted subspaces of X, where B（H） denotes the C＊-algebra of bounded linear operators on a separable Hilbert space H.     

相似不变子空间和保相似线性映射

本文给出了可分无限维Hilbert空间H上有界线性算子全体B(H)中的相似不变子空间的构造,同时给出了B(H)上双边保相似线性映射的表示.     

Similarity-Invariant Subspaces and Similarity-Preserving Linear Maps

In this paper, the similarity-invariant subspaces of B(H), which is the Banach algebra of all bounded linear operators on a separable infinite-dimensional Hilbert space H, are completely characterized and the representations of bounded linear maps on B(H) which preserve similarity in both directions are given. Received November 3, 1999, Revised September 20, 2000, Accepted February 5, 2001     

保持算子乘积投影的线性映射

设B(H)是复Hilbert空间H上的有界线性算子全体且dim H≥2.本文证明了B(H)上的线性满射φ保持两个算子乘积非零投影性的充分必要条件是存在B(H)中的酉算子U以及复常数λ满足λ~2=1,使得φ(X)=λU~*XU,(?)X∈B(H).同时也得到了线性映射保持两个算子Jordan三乘积非零投影的充分必要条件.     

非齐型空间上分数型Marcinkiewicz积分算子的加权估计

令（X，d，μ）为满足所谓上倍双倍条件和几何双倍条件的度量测度空间.设M_β，ρ，q为（X，d，μ）上的分数型Marcinkiewicz积分算子.在本文中，作者证明了若β ∈[0，∞），ρ ∈（0，∞），q ∈（1，∞）且M_β，ρ，q在L²（μ）上有界，则M_β，ρ，q是从加权Lebesgue空间L^p（w）到加权弱Lebesgue空间L^p，∞（w）上有界和从加权Morrey空间L^p，κ，η（ω）到加权弱Morrey空间WL^p，κ，η（ω）上有界.     

从Hardy空间到加权Bloch型空间的加权复合算子

研究了单位圆上从Hardy空间到α-Bloch空间的加权复合算子uC_φ的有界性和紧性.分别给出从H~p空间到β~α空间和β_0~α空间的算子uC_φ的有界性和紧性的充分和必要条件.     

Surjective isometries on spaces of vector valued continuous and Lipschitz functions

For X a compact Hausdorff topological space and F a strictly convex and reflexive Banach space we characterize the surjective isometries of certain subspaces of C(X, F). It follows from this characterization that surjective isometries on spaces of vector valued Lipschitz functions equipped with a p-norm are also weighted composition operators.     

Spaces of operator-valued measures on topological spaces

Summary Let X be a completely regular space and E a locally convex space. We study a space M(B, E′) of E′-valued measures defined on the algebra generated by the zero subsets of X. We also study certain subspaces of M(B, E′). Entrata in Redazione il 20 ottobre 1976.     

关于Banach空间的遗传不能分解和商遗传不能合成性质

该文说明遗传不能分解空间上的黎斯算子类构成了最大、非平凡的算子理想，简化了Gowers和Maurey关于这类空间上算子构成的推证．应用对偶原理，引入商遗传不能合成的概念，讨论商遗传不能合成的Banach空间上的算子构成，得到了相应的一些结果．     

B(X)上保持约当积的固定点的满射

设B(X)是维数大于等于3的复Banach空间X上有界线性算子全体构成的代数.设A∈B(X),若Ax=x,则称x∈X是算子A的固定点.Fix(A)表示A的所有固定点的集合.本文刻画了B(X)上保持算子的Jordan积的固定点的满射.     

Asymptotic T_u-Toeplitzness of weighted composition operators on H~2

Given a unilateral forward shift S acting on a complex,separable,infinite dimensional Hilbert space H,an asymptotically S-Toeplitz operator is a bounded linear operator T on H satisfying that{S~(*n)T S~n}is convergent with respect to one of the topologies commonly used in the algebra of bounded linear operators on H.In this paper,we study the asymptotic T_u-Toeplitzness of weighted composition operators on the Hardy space H~2,where u is a nonconstant inner function.     

Homogeneity Properties of Some ℓ1-Spaces

Let M be a family of subspaces of a metric space X. The space X is M-homogeneous if any isometry between two subspaces in M can be extended to an isometry of X. In the case when M is the family of all subspaces of X, the space X is said to be fully homogeneous. We show that the space Lⁿ, where L is a fully homogeneous subspace of ℝ, is R-homogeneous where R is the family of subspaces that are products of subsets of L.     

多圆柱上Bergman空间到Bloch空间的复合算子

设qo是单位多圆柱Dn到自身的—个全纯映射,ψ是Dn上的—个全纯函数．本文研究单位多圆柱上从Bergman空间Ap（Dn）到Bloch空间β（Dn）的加权复合算子Tψ,ψ通过全纯映射ψ和全纯函数ψ的函数特征。分别给出了单位多圆柱上从Bergman空间AP（Dn）到Bloch空间β（Dn）的加权复合算子Tψ,ψ有界性和紧性的充分必要条件．     

Bilinear forms on exact operator spaces andB(H)⊗B(H)

LetE, F be exact operator spaces (for example subspaces of theC ^*-algebraK(H) of all the compact operators on an infinite dimensional Hilbert spaceH). We study a class of bounded linear mapsu: E →F ^* which we call tracially bounded. In particular, we prove that every completely bounded (in shortc.b.) mapu: E →F ^* factors boundedly through a Hilbert space. This is used to show that the setOS _n of alln-dimensional operator spaces equipped with thec.b. version of the Banach Mazur distance is not separable ifn>2. As an application we whow that there is more than oneC ^*-norm onB (H) ? B (H), or equivalently that $$B(H) \otimes _{\min } B(H) \ne B(H) \otimes _{\max } B(H),$$ which answers a long standing open question. Finally we show that every “maximal” operator space (in the sense of Blecher-Paulsen) is not exact in the infinite dimensional case, and in the finite dimensional case, we give a lower bound for the “exactness constant”. In the final section, we introduce and study a new tensor product forC ^*-albegras and for operator spaces, closely related to the preceding results.     

Smooth points of certain operator spaces

Let B(H) denote the Banach space of all bounded linear operators on a separable, infinite dimensional Hilbert space H, and let C be the ideal of compact operators on H. It is shown that the unit ball of the Calkin algebra B(H)/C has no smooth points. We use this to determine the smooth points of the unit ball of B(H).     

包含广义逆的算子乘积的谱

给定三个算子A,B,C∈ B(H),其中算子B的值域R(B)是闭的,利用算子矩阵分块技巧给出了∪σ(AB(1))C)=C的充分必要条件,其中σ(D)是算子D ∈B(H)的B(1) ∈B{1}谱,B{1}={X∈B(H):B×B=B}.     

On the topological linear spaces whose subspace lattices are modular

LetX be a topological linear space and letL(X) be a lattice of all closed subspaces ofX. We show that in many cases the modularity ofL(X) implies that every bounded subset ofX is finite-dimensional. We derive some topological consequences of the latter result. Due to the significance of the modularity condition forL(X) in quantum axiomatics and elswhere (see [1,14,15]) results also might find application outside the realm of topological linear spaces.     

多圆盘的加权Bergman空间上的不变子空间和约化子空间

本文主要研究多圆盘的加权Bergman 空间上的不变子空间和约化子空间, 给出了某些解析Toeplitz 算子的极小约化子空间的完全刻画, 以及一类解析Toeplitz 算子Tzi (1≤i≤n) 的不变子空间的Beurling 型定理.     

A sharp bound for the Castelnuovo-Mumford regularity of subspace arrangements

We show that the ideal of an arrangement of d linear subspaces of projective space is d-regular in the sense of Castelnuovo and Mumford, answering a question of B. Sturmfels. In particular, this implies that the ideal of an arrangement of d subspaces is generated in degrees less than or equal to d.