一类具有弱无孔性质的c*-代数

证明了一类C~*-代数的弱无孔性质可以遗传到通过此类C~*-代数迹逼近后得到的C~*-代数中.同时证明了具有弱无孔性质的C~*-代数经过具有迹Rokhlin性质的有限群作用后得到的交叉积C~*-代数也具有弱无孔性质。     

第6卷 B 辑 第1期(1985)目录和提要

c~*-代数上非单位的正线性映象李炳仁通常讨论 C~*-代数到 C~*代数的正线性映象总假定它把单位元变作单位元.本文讨论的 C~*-代数不要假定有单位元.主要结果有两个:1)如果Φ是 C~*-代数 A 到 C~*-代数 B 的正线性映象,如同 A 上的正线性泛函那样,Φ的范数有如下的表达式‖Φ‖=sup{‖Φ(a)‖|a∈A_+,‖a‖≤1}=‖Φ(v_l)‖=‖Φ(v_l~2)‖,这里{v_l}是 A 的一个逼近单位元;2)如果Φ是 C~*-代数 A 到 C~* -代数 B 的 n-正线性映象,并且     

算子代数分类浅探

本文介绍半个多世纪以来算子代数主要是C~*-代数分类理论发展的概况;叙述了一系列当年的主要结果及相关的主要概念;也谈到了目前世界上最新的包括作者最近的关于单顺从C~*-代数的分类定理以及有关的应用,并列出了一些今后C~*-代数的发展课题.     

C~*-代数的Murray-von Neumann分类理论的抽象架构

Murray和von Neumann在对W~*-代数进行分类工作时,主要的工具是刻画W~*-代数中的投影的性质(事实上,W~*-代数是由投影所生成的).因为一般的C~*-代数可能不包含任何非零的投影,所以不能将Murray和von Neumann的方法,直接地应用到C~*-代数上来得出分类理论.本文作者在最近的两项工作中,分别使用C~*-代数的开投影和正元来代替投影,得到两套平行的Murray-von Neumann式的分类理论.本文在简单描述了这两套分类理论之后,将会给出一个一般的分类架构,它可以用来得出好些C~*-代数的分类理论(包括我们之前的两套理论),我们也会通过它来讨论各种分类理论之间的等价性,并给出之前两套理论的细化.     

迹分解秩(英文)

首先引入迹分解秩的概念,具有这个结构的稳定有限的顺从C~*-代数非常多.这个概念和Elliott的用K-理论来分类顺从C~*-代数的分类计划有重要的联系.然后研究C~*-代数扩张.设0→I→A-→A/I→0是C~*-代数的一个短正合序列,其中A有单位元.假设I有分解秩k,A/I有迹分解秩k,那么如果扩张是拟对角的,本文将证明A的迹分解秩不超过k.     

可能行无限图C~*-代数

本文研究可能行无限有向图的C~*-代数。对于一个可能行无限的有向图E,通过引进集合S(μ,v),将行无限点上的算子拓扑强收敛关系代数化表示出来,并由此构造了一个结构丰富的非零*-代数H_E;进而利用H_E证明了一个由Cuntz-Krieger E-族{s_e,p_v}生成的泛C~*-代数 C~*(E)的存在性,并且证明了H_E和 C~*(E)在图同构意义下不依赖于E的选择,从而是可能行无限有向图的同构不变量。     

一类Smale空间上的C~*-代数自同构的熵

Ian Putnam利用Smale空间上的渐近等价关系定义了广群C~*-代数及其典则自同构.本文在零维Smale空间的情形下,计算此类C~*-自同构的逼近熵,证明了相应C~*-动力系统关于CNT熵和逼近熵的"变分原理"成立.由此推演出此类Smale空间上的Bowen测度诱导的C~*-代数上的态是此典则自同构的唯一平衡态.     

性质S的注记

本文刻划了性质S的几个等价条件。在一定条件下,证明了性质S可以遗传到子C~*-代数上去,从而部分地肯定回答了Lance,E.C.的一个问题。另外,还讨论了群在具有性质S的C~*-代数上的作用。     

迹稳定秩1的C~*-代数的稳定有限性与弱迹稳定秩1

主要给出了迹稳定秩1的C~*-代数的稳定有限性,证明了如果A是有单位元迹稳定秩1的C~*-代数,则A是稳定有限的,引入了弱迹稳定秩1的定义,并且证明了如果有单位元的C~*-代数A是迹稳定秩1的,则A是弱迹稳定秩1的．对于单的具有SP性质的有单位元的C~*-代数A,如果A是弱迹稳定秩1的,则A是迹稳定秩1的．同时给出了迹稳定秩1的C~*-代数的一个等价条件,证明了一个有单位元的可分的C~*-代数A是迹稳定秩1的,等价于A=(t_4)limn→∞(A_n,p_n),其中tsr(A_n)=1．     

归纳极限与积C~*-代数的α-比较性

?对于C~*-代数归纳极限A=(lim→)(A_n,φ_(m,n)(其中A_n?A_(n-1)?A且φ_(n,n-1):A_n→A_(n+1)为嵌入映射),若A_n人为具有α-比较的单的含单位元的稳定有限的C~*-代数,则A具有α-比较性;若A_λ(?_λ∈Λ)具有α-比较性,则积C~*-代数(Πλ∈A)A_λ具有α-比较性,特别地,和C~*-代数(λ∈A)A_λ具有α-比较性.     

Fell bundles over groupoids

We study the C*-algebras associated to Fell bundles over groupoids and give a notion of equivalence for Fell bundles which guarantees that the associated C*-algebras are strongly Morita equivalent. As a corollary we show that any saturated Fell bundle is equivalent to a semi-direct product arising from the action of the groupoid on a C*-bundle.

     

Morita equivalence of C*-correspondences passes to the related operator algebras

We revisit a central result of Muhly and Solel on operator algebras of C*-correspondences. We prove that (possibly non-injective) strongly Morita equivalent C*-correspondences have strongly Morita equivalent relative Cuntz–Pimsner C*-algebras. The same holds for strong Morita equivalence (in the sense of Blecher, Muhly and Paulsen) and strong Δ-equivalence (in the sense of Eleftherakis) for the related tensor algebras. In particular, we obtain stable isomorphism of the operator algebras when the equivalence is given by a σ-TRO. As an application we show that strong Morita equivalence coincides with strong Δ-equivalence for tensor algebras of aperiodic C*-correspondences.     

INVARIANTS UNDER STABLE EQUIVALENCES OF MORITA TYPE

The aim of this article is to study some invariants of associative algebras under stable equivalences of Morita type.First of all,we show that,if two finite-dimensional selfinjective k-algebras are sta...     

Crossed Products of pro-C*-Algebras and Morita Equivalence

We introduce the notion of strong Morita equivalence for group actions on pro-C* -algebras and prove that the crossed products associated with two strongly Morita equivalent continuous inverse limit actions of a locally compact group G on the pro-C* -algebras A and B are strongly Morita equivalent. This generalizes a result of F. Combes [2] and R.E. Curto, P.S. Muhly, D.P. Williams [3]. This research was supported by CEEX grant-code PR-D11-PT00-48/2005 from The Romanian Ministry of Education and Research.     

Explicit Equivalence Bimodules for Rotation Algebras

The C*-algebras associated with irrational rotations are Morita equivalent if and only if the rotation parameters belong to the same orbit under the action of GL(2, Z). In this note, we suggest explicit type II representations such that the bimodule is dense in the corresponding Hilbert space. Bibliography: 4 titles. __________ Published in Zapiski Nauchnykh Seminarov POMI, Vol. 307, 2004, pp. 175–188.     

On the Morita Equivalence of Tensor Algebras

We develop a notion of Morita equivalence for general C^*-correspondencesover C^*-algebras. We show that if two correspondences are Moritaequivalent, then the tensor algebras built from them are stronglyMorita equivalent in the sense developed by Blecher, Muhly andPaulsen. Also, the Toeplitz algebras are strongly Morita equivalentin the sense of Rieffel, as are the Cuntz–Pimsner algebras.Conversely, if the tensor algebras are strongly Morita equivalent,and if the correspondences are aperiodic in a fashion that generalizesthe notion of aperiodicity for automorphisms of C^*-algebras,then the correspondences are Morita equivalent. This generalizesa venerated theorem of Arveson on algebraic conjugacy invariantsfor ergodic, measure-preserving transformations. The notionof aperiodicity, which also generalizes the concept of fullConnes spectrum for automorphisms, is explored; its role inthe ideal theory of tensor algebras and in the theory of theirautomorphisms is investigated. 1991 Mathematics Subject Classification:46H10, 46H20, 46H99, 46M99, 47D15, 47D25.     

Equivalence of the Stone-Weierstrass conjectures for C* and JB*-algebras

We prove that the Stone-Weierstrass conjectures for C*-algebras and JB*-algebras are equivalent.     

Morita equivalence and Pedersen ideals

We show that two -algebras are strongly Morita equivalent if and only if their Pedersen ideals are Morita equivalent as rings with involution.

     

ON THE APPROXIMATELY SIMILARITY OF OPERATORS

1.IntroductionInwhatfollows,allofHilbertspacesappearedinthispaperareinfinite-dimensionalseparablecomplexHilbertspace.IfHisaHilbertspace,thenC(n)denotestheC*--algebraofallboundedlinearoperatorsonHandK(H)denotesthesetofcompactoperatorsonn.TwooperatorsSandTarecalledapproximatelyequivalentifthereisasequenc{Un}ofunitaryoperatorssuchthatlIU:SUn--Tll-0(n-- co).SimilarlytwooperatosSandTareapproximatelysimilarifthereisasequence{Vn}ofinvertibleoperatorswithsup(llVn11,11VJ'11)相似文献