On the K0 groups of nest algebras

In this paper we compute the K ₀ group of any nest subalgebra of ().     

Synthesis,Crystal Structure and Third‐order Nonlinear Optical Properties of Nest‐shaped Cluster [CuBr(bpy)2] [MoOS3Cu3‐Br2(bpy)]

Nest‐shaped cluster [CuBr(bpy)₂][MoOS₃Cu3Br₂(bpy)] was synthesized by the treatment of (NH₄)₂ MOO₂S₂, CuBr and Et₄NBr with bpy (2,2′‐bipyridyl) in CH₃CN. Its structure has been characterized by X‐ray diffraction; monoclinic, space group P2₁/n ‐ with a = l.0092(4), b = 2.6347(7), c = 1.4087(3) nm, β = 91.744(9)°, V = 3.7438 nm³, Z=4, and final R = 0.051, R_w = 0.053. It consists of two parts: nest‐shaped structural unit [MoOS₃Cu₃Br₂(bpy)] and complex ion [CuBr(bpy)²]⁺. We determined its third‐order nonlinear optical (NLO) properties with a 7‐ns pulsed laser at 532 nm. The duster exhibits strong NLO refractive behavior, its third‐order susceptibility χ⁽³⁾ was calculated to be 2.7 · 10^?11 esu in a 7.8 · 10^?4 g/cm³ DMF solution. The value is comparable to those of inorganic dusters.     

实Nest代数上的广义Jordan~*-左导子

设H是实Hilber空间, (?)是B(H)中含恒等算子I的算子代数,若(?) 是从(?)到B(H)的线性映射,如果(?)满足对任意的T∈(?),有(?)(T2)=T*(?)(T)+ (?)(T)T-T*(?)(I)T,则称(?)是一个广义Jordan*-左导子;如果(?)满足对任意的T∈(?), 有(?)(T)(ker(T))(?)ran(T*),则称(?)是一个左*-核值保持映射.本文主要获得了如下 结果: Nest代数上每个弱算子拓扑连续的左*-核值保持映射是广义Jordan*-左内 导子,即存在A,B∈B(H),使得对任意的T∈(?),有(?)(T)=T*A+BT.特别地,(?) 也是一个广义Jordan*-左导子.     

von Neumann代数中套子代数的摄动

本文主要讨论ｖｏｎ　Ｎｅｕｍａｎｎ代数中套子代数的摄动．给出了因子ｖｏｎ　Ｎｅｕｍａｎｎ代数中套相似的一个充分条件．证明了任何因子ｖｏｎ　Ｎｅｕｍａｎｎ代数中相邻的套子代数经由一个邻近于单位元的可逆算子是相似的．     

TENSOR PRODUCTS OF JACOBSON RADICALS IN NEST ALGEBRAS

This paper studies the tensor product RN RM of Jacobson radicals in nest algebras, and obtains that RN RM = {T∈B(H1 H2) : T(N M)(?)N_ M_, N∈N,M∈M}; and based on the characterization of rank-one operators in RN RM,it is proved that if N, M are non-trivial then RN RM=R if and only if N, M are continuous.     

套子代数上线性映射的Lie不变子空间

本文引入了Banach代数上线性映射的Lie不变子空间,给出了因子VonNeumann代数中套子代数上以导子空间为Lie不变子空间的线性映射的一般形式,研究了Lie导子与Lie自同构的概念及了Lie导子与Lie自同构半群的关系.     

连续套代数中强不可约算子的酉轨道闭包

在这篇文章里,N表示连续套,且我们完全刻划了T（N）中强不可约算子的酉轨道闭包．     

The Distance to Upper Triangular Operator Spaces of Von Neumann Algebras

Ｔｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒ，ｔｈｅｎｏｎｚｅｒｏＨｉｌｂｅｒｔｓｐａｃｅＨｕｎｄｅｒｃｏｎｓｉｄｅｒａｔｉｏｎｉｓｃｏｍｌｅｘａｎｄｓｅｐａｒａｂｌｅ．ＬｅｔＢ（Ｈ）ｂｅｔｈｅｓｅｔｏｆａｌｌｉｎｅａｒｂｏｕｎｄｅｄｏｐｅｒａｔｏｒｓｏｎ...     

自反算子代数的导子和同构

本文证明了：Ｂａｎａｃｈ空间上完全分配格代数间的导子都是自动连续的；进而证明了套代数的可加导子是内的，套代数间的代数同构是自动连续的、空间的