Pro-C~*-代数的顺从性和核性(英文)  

Amenability and Nuclearity for Pro-C*-Algebras

作　　者：许天周[1] 李炳照[1] 赵雨耿[1] 

机构地区：[1]北京理工大学应用数学系,北京中国100081

出　　处：《数学进展》2003年第3期334-340,共7页Advances in Mathematics（China）

摘　　要：研究了Pro-C*-代数的顺从性和核性.主要证明了(1)顺从Pro-C*-代数的闭理想是顺从的;(2)核Pro-C*-代数类对归纳极限封闭;(3)交换σ-C*-代数和核C*-代数都是核σ-C*-代数并且核σ-C*-代数类对于商运算、张量积运算和可数逆向极限封闭.进一步得到核σ-C*-代数的扩张保持核性的条件.Any closed ideal of an amenable Pro-C*-algebra (inverse limit of C*-algebras) is amenable. The class of nuclear Pro-C'-algebras is closed under inductive limits. In particular, the class of nuclear σ-C*-algebras contains all commutative σ-C*-algebras and all nuclear C*-algebras, and is closed under quotients, tensor products and countable inverse limits. Extensions of nuclear σ-C* algebras by nuclear σ-C*-algebras axe themselves nuclear.

关 键 词：Pro-C^＊-代数 顺从性 核性 闭理想 归纳极限 封闭性 σ-C^＊-代数 BANACH代数 lmc-C^＊-代数 

分 类 号：O177.5[理学—数学]