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.     

因子von Neumann代数上的非线性Lie导子

设M是作用在维数大于2的复可分Hilbert空间,■上的因子von Neumann代数.证明了因子von Neumann代数M上的每一个非线性Lie导子具有形式A→ψ(A)+h(A)I,其中:.M→M是可加的导子,h:M→C是非线性映射且对所有A,B∈M,有h(AB-BA)=0.     

Sarason’s interpolation theorem for analytic crossed products

Saito (Math. Proc. Camb. Phil. Soc., 117, 11–20, 1995) proved Sarason’s interpolation theorem for an analytic crossed product determined by a finite von Neumann algebra. We extend this result without the assumption that the von Neumann algebra is finite.     

自反子空间格的表示和运算

证明了von Neumann 代数的子空间格的自反性和KS- 性都不依赖于该von Neumann 代数的正规忠实*- 表示; 引入了von Neumann 代数及所含子空间格的半自由积运算, 证明了两子空间格的半自由积同构于它们的直和.     

von Neumann代数中套子代数上的Lie同构

本文给出因子von Neumann代数中的幂等算子在广义Lie积下的一个刻画; 得到因子von Neumann代数中套子代数的幂等算子在Lie积下的一个特征．作为应用, 研究了因子von Neumann代数中套子代数上的Lie同构,并证明因子von Neumann 代数中套子代数之间的Lie同构,要么是同构与广义迹之和,要么是负反同构与广义迹之和．     

具有分解性质的次对角代数

设M是σ-有限的von Neumann代数,21是M的具有分解性质的次对角代数,即对任意可逆算子T∈M,都存在西算子U∈M及可逆算子A∈21∩21~(-1),使得T=UA,本文证明了21的代数换位是自伴的,同时也证明了21中的可逆算子群是σ-弱连通集。     

保正交性或与|·|~k交换的可加映射

设H是复Hilbert空间,B（H）表示H上所有有界线性算子构成的代数.本文刻划了B（H）上保正交性的可加映射和von Neumann代数上与运算|·|k交换的可加映射.     

von Neumann代数的T-局部导子

In this paper, we introduce the concept of T-local derivations and obtain the main result: each T-local derivation of a von Neumann algebra A into a dual A-bimodule M is a T-derivation, where T is an endomorphism of A to A.     

因子Von Neumann代数中套子代数上的局部3-上循环

证明了因子von Neumann代数中的套子代数到其单位对偶双模内的每个弱连续的局部3-上循环都是3-上循环.     

A weak* similarity degree characterization for injective von Neumann algebras

In this note, we show that a von Neumann algebra M is injective if and only if the weak*similarity degree d*(M) ≤ 2.