C~*-algebra

An introduction to the definition of the simple tracial limit of C~*-algebra is first made in this paper.

引进了简单迹极限的相关概念,简单介绍了与C*C*代数SP性质密切相关的F性质,并且得到了非基本的单的具有SP性质的C*C*代数具有F性质。

A conclusion is drawn that the K0 groups of simple C*C*-algebras which possess tracial-NG properties have NG properties.

研究C*-C*代数K0群的弱无孔性质、Riesz内插值性质,把这2种性质统称为NG性质;并且引入具有迹-NG性质的C*-C*代数概念。

One *-isomorphism of C*C*-algebras must be (completely) isometric map, but the inverse is not.

C*-C*代数的*-同构一定是(完全)等距映射,反之不然。

The paper also presents the answer to the lifting problems of the projections of the corresponding quotient C*C*-algebras.

利用C*-C*代数I具有由投影组成的近似单位元的条件,给出了一类M(I)中以I作为理想的C*-子C*代数,证明每一个这样C*-子C*代数的任何元素,均为弱拟对角化以及这些C*-子C*代数之间的关系,同时回答了相应商C*代数投影的提升问题。

In this paper,we show that if A is a simple unital C~*-algebra with tracial stable rank one and SP property,then A has cancellation of projections.

证明了如果A是单的有单位元的C*-C*代数满足Tsr(A)=1,并且具有SP性质(对于A的任意非零可传C-子C*代数B,B都包含一个非零的投影),则A具有投影的消去律。

This paper studies the properties of a matrix-trace on C~*-algebra M_n(A) which is a positive linear mapping τ∶M_n(A)→A such that τ(u~*au)=τ(a)(a∈(M_n(A),)u∈U(M_n(A))) and τ(a~2)≤(τ(a))~2(a≥0), and obtains some inequalities.

C*-C*代数Mn(A)上矩阵迹是一个正线性映射τ∶Mn(A)→A且满足τ(u*au)=τ(a)(a∈Mn(A),u∈U(Mn(A)))及τ(a2)≤(τ(a))2(a≥0)。

The α-Power Geometric Mean and Generalized Spectral Geometric Mean of Two Positive Definite Elements in a C~*-algebra;

引入并研究了C*-C*代数中两个正定元a与b的α-幂几何平均gα(a,b)与广义谱几何平均Eα(a,b),且由此证明了一系列相关的性质和定理。

In this paper,the pure state ranges of non-commuting C~*-algebras are discussed and a representation of the essential pure state range of a pair of elements in the tensor products algebra of non-commuting C~*-algebras are obtained.

讨论了非交换C*-C*代数的谱与纯态值域,得到了C*-C*代数张量积中两个元的本质纯态值域的表示。

Extension of Tracial Topological Rank of C~*-algebras;

给出了具有TR(S)性质C*-C*代数类的概念,作出了一个关于迹拓扑秩的推广,得到定理2,即A是有单位元的单的C*-C*代数,若A具有TR(S1)性质,则tsr(A)=1。

Fourier Transformation and Vinogradov Inequality of C-algebras;

C-C*代数上的Fourier变换和C-C*代数上的Vinogradov不等式(英文)

On the Covariant Isomorphism of Crossed-product C-algebras of the Form K（l~2（Z_+~2)）×_(αθ)Z;

C-C*代数交叉积K(l~2(Z_+~2))×_(αθ)Z的协变同构(英)

Toeplitz C-algebras on Reinhardt domain with periodical boundry;

具有周期边界的Reinhardt域上的Toeplitz　C－C*代数

Several equivalent conditions for infinite positive elements in C*C*-algebras are studied in this paper.

讨论了判定C*-C*代数中的正元是无限元的几个等价条件,并且证明了E。

In this note,for a C*C*-algebra A,we study the properties of a matrix-trace on the C*C*-algebra Mn(A) which is a positive linear mapping τ:Mn(A)→A,such that τ(u*au)=τ(a)(a∈Mn(A)),u∈U(Mn(A)) and τ(a2)≤(τ(a))2(a≥0),and obtain some inequalities on arithmetic-geometric mean.

对于C*-C*代数A,C*-C*代数Mn(A)上矩阵迹是一个正线性映射τ:Mn(A)→A,满足τ(u*au)=(τa)(a∈Mn(A)),u∈U(Mn(A))和τ(a2)≤(τ(a))2(a≥0)。

Equivalence has very important effect in C*-Algebra.

寻找等价关系是研究不变量的一种方法,为了使大家更好的认识和学习C*-C*代数,我们在本文研究了算子C*代数中经常用到的C*代数等价、酉等价、同伦等几种等价之间的关系。