Scattered elements of Banach algebras

被引：2
|
作者：
Cao, Peng [1 ,2 ]
机构：
[1] Beijing Inst Technol, Sch Math, Beijing 100081, Peoples R China
[2] Minist Educ, Key Lab Math Informat & Behav Semant, Beijing 100081, Peoples R China
来源：
STUDIA MATHEMATICA | 2013年 / 214卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Jacobson radical; scattered radical; scattered element;
D O I：
10.4064/sm214-2-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A scattered element of a Banach algebra A is an element with at most countable spectrum. The set of all scattered elements is denoted by S(A). The scattered radical R-sc(A) is the largest ideal consisting of scattered elements. We characterize in several ways central elements of A modulo the scattered radical. As a consequence, it is shown that the following conditions are equivalent: (i) S(A) + S(A) subset of S(A); (ii) S (A) S (A) subset of S (A); (iii) [S (A), A] subset of R-sc(A).
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页码：195 / 200
页数：6
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