Minimal elements related to a conditional expectation in a C*-algebra

被引：3

作者：

Zhang, Ying ^{[1
]}

Jiang, Lining ^{[1
]}

机构：

[1] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

来源：

ANNALS OF FUNCTIONAL ANALYSIS | 2023年 / 14卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Minimal elements; Conditional expectation; Positive modification; The unilateral shift; The backward shift; APPROXIMATION;

D O I：

10.1007/s43034-023-00252-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let A be a C*-algebra and B a C*-subalgebra of A such that there is a conditional expectation from A onto it. Using the property of positive modification, this paper characterizes an element a is an element of A satisfying(sic)a(sic) = inf{(sic)a +b(sic) : b is an element of B}.Such an a is called B-minimal. As an application of these results it is shown that both the unilateral shift and the backward shift are D(B(l(2)))-minimal, where D(B(l(2))) is the set of diagonal operators in B(l(2)), and thus provides new examples of minimal operators which are neither hermitian nor compact.

引用

页数：14

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