τ-可测正算子生成的交换子的若干不等式

设M是具有正规忠实的半有限迹τ的von Neumann代数,‖.‖ρ是任意非交换Banach函数空间范数,‖.‖是M上的通常范数.证明了若A和B是τ-可测正算子,X∈M,则‖AX-XB‖ρ≤‖X‖‖AB‖ρ.还证明了若A,B是M中的正算子,X是τ-可测算子,则‖AX-XB‖ρ≤max(‖A‖,‖B‖)‖X‖ρ.由此得到了若A∈M是正算子,X是τ-可测正算子,则‖AX-XA‖ρ≤1/2‖A‖‖XX‖ρ.     

非交换的Kolmogorov不等式和Zygmund不等式

In this paper,we discuss some properties of distribution functions of τ-measurable operators and obtain non-commutative analogue of Kolmogorov inequality and Zygmund inequality.     

关于依测度拓扑收敛

给出了τ-可测算子的依测度收敛的充要条件和Hilbert空间内依测度收敛的充要条件．     

τ-可测算子迹的不等式

设m是具有忠实正规半有限迹τ的Hilbert空间上的一个半有限von Neumann代数.隶属于m的—个闭稠定算子x称为τ可测,如果存在常数λ≥0使得τ（e｜x｜（λ,∞））〈∞.将一些很有用的已知的Hilbert空间算子迹的不等式推广到τ-可测算子迹.特别是这些不等式蕴涵了n-元τ-可测算子的Clarkson不等式.同时还给出了τ-可测算子的广义平行四边形法则.     

Harby空间上的复合算子

本文讨论n维复单位球的Harby空间上的复合算子，主要是利用Banach代数和n维单位球上解析函数的理论，给出了这类空间上复合算子的一个特征，证明了复合算子可逆的充要条件是其符号函数属于单位球的自同构群，并且对复合算子的范数作出了估计。     

理想的Riesz扩张

本在有单位元e的交换Banach代数B中定义了其闭理想A的Riesz扩张R，并证明了R＝A＋Q的充分条件为A={a,a∈A}在局部凸拓扑{|ρ（x)|:ρ∈Ω}下闭，其中Q为B的根基，x为x（∈B）在商映射θ：B→B/Q下的像，Ω为B的谱空间，ρ(x)=ρ(x),↓Ax∈B,ρ∈Ω。     

关于G-M成果研究的若干新动态Ⅱ--与G-M型空间相关的算子

结合自己的工作，对Gowers-Maurey系列成果获Fields奖以来的研究的新动态作一综述，该是下篇，主要讨论与G-M型空间相关的算子，包括可通过G-M型空间分解的算子，G-M型空间上的算子理想与算子构成，G-M型空间上的算子谱理论等。     

关于一类随机非线性算子方程的若干问题的研究（英文）

本文推广了两个重要的不等式,并且利用随机不动点指数理论研究了一类随机非线性算子方程的随机解的存在性问题,主要结果推广了著名的Altman定理.最后给出主要结果在随机非线性积分方程中的一个应用.     

四元数值函数空间L~1上有界右线性算子的积分表示

基于复Hilbert空间上丰富的算子理论,四元数函数空间与复值函数空间的区别和联系,将讨论四元数值函数空间L~1上有界右线性算子的积分表示.     

Some Inequalities in Classical Spaces with Mixed Norms

We consider some inequalities in such classical Banach Function Spaces as Lorentz, Marcinkiewicz, and Orlicz spaces. Our aim is to explore connections between the norm of a function of two variables on the product space and the mixed norm of the same function, where mixed norm is calculated in function spaces on coordinate spaces, first in one variable, then in the other. This issue is motivated by various problems of functional analysis and theory of functions. We will currently mention just geometry of spaces of vector-valued functions and embedding theorems for Sobolev and Besov spaces generated by metrics which differ from L ^p. Our main results are actually counterexamples for Lorentz spaces versus the natural intuition that arises from the easier case of Orlicz spaces (Section 2). In the Appendix we give a proof for the Kolmogorov–Nagumo theorem on change of order of mixed norm calculation in its most general form. This result shows that L ^p is the only space where it is possible to change this order.     

Preduals of von Neumann Algebras

Proofs of two assertions are sketched. 1) If the Banach space of a von Neumann algebra A is the third dual of some Banach space, then the space A is isometrically isomorphic to the second dual of some von Neumann algebra A and the von Neumann algebra A is uniquely determined by its enveloping von Neumann algebra (up to von Neumann algebra isomorphism) and is the unique second predual of A (up to isometric isomorphism of Banach spaces). 2) An infinite-dimensional von Neumann algebra cannot have preduals of all orders.     

On K_0-groups of operator algebras on Banach spaces

This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X2 is not a sufficient condition of K0(B(X)) = 0.     

On Commutators of Idempotents

It is shown that a pair of idempotent operators on a Banach space is triangularizable if their commutator is nilpotent. Moreover, if every operator on Hilbert space has an invariant subspace, then a pair of idempotents on Hilbert space is triangularizable if their commutator is quasinilpotent. These results are generalized from idempotents to quadratic operators.     

On Commutators of Idempotents

It is shown that a pair of idempotent operators on a Banach space is triangularizable if their commutator is nilpotent. Moreover, if every operator on Hilbert space has an invariant subspace, then a pair of idempotents on Hilbert space is triangularizable if their commutator is quasinilpotent. These results are generalized from idempotents to quadratic operators.     

广义分数次积分多线性交换子的端点估计

设函数b=（b1,b2,…,bm）和广义分数次积分L-a／2（0〈α〈n）,它们生成多线性算子定义如下 Lb -a/2 f = [bm …, [b2[b1, L-a/2]],…, ]f,其中m ∈ Z＋ , bi ∈ Lipβi （0 〈βi 〈 1）,其中（1≤i≤m）．将讨论Lb -1a/2。从Mp^q（Rn）到Lip（α＋β-n/ q） （ Rn ）和q^q （ Rn ）到BMO（Rn）的有界性．