包含紧算子理想的Toeplitz算子代数的刻画(英文)  

A Character of Toeplitz Algebras Containing the Ideal of Compact Operators

作　　者：许庆祥[1] 

机构地区：[1]上海师范大学数学科学学院

出　　处：《数学进展》2001年第5期432-434,共3页Advances in Mathematics（China）

基　　金：Supported by the NSFC (No.19901019) and the Youth Science Foundation of Shanghai Higher Education (No. 98QN75)

摘　　要：设Ｇ为一个ｔｏｒｓｉｏｎ－ｆｒｅｅ的离散群，（Ｇ，Ｇ＋）为一个拟序群．记 ＴＧ＋（Ｇ）为相应的Ｔｏｅｐｌｉｔｚ算子代数，Ｋ（２（Ｇ＋））为２（Ｇ＋）上的紧算子全体．本文证明了 Ｋ（２（Ｇ＋））ＴＧ＋（Ｇ）当且仅当下列两个条件同时满足：（１）（Ｇ，Ｇ＋）为一个序群；（２）Ｇ中存在一个最小的正元．Let G be a discrete torsion-free group and (G, G+) a quasi-ordered group. Let TG+ (G) be the corresponding Toeplitz algebra. In this note, we show that TG+ (G) contains the ideal of compact operators on 2(G+) if and only if the following two conditions are satisfied: (1) (G, G+) is an ordered group; (2) G admits a least positive element.

关 键 词：离散拟序群 TOEPLITZ算子 紧算子 torsion-free离散群 序群 最小正元 

分 类 号：O177.5[理学—数学]