Operator algebras with contractive approximate identities, II

被引：22

作者：

Blecher, David P. ^{[1
]}

Read, Charles John ^{[2
]}

机构：

[1] Univ Houston, Dept Math, Houston, TX 77204 USA

[2] Univ Leeds, Dept Pure Math, Leeds LS2 9JT, W Yorkshire, England

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2013年 / 264卷 / 04期

基金：

美国国家科学基金会;

关键词：

Operator algebra; Approximate identity; Proximinality; Peak set; Peak interpolation; Operator with positive real part; Accretive operator; Noncommutative topology; Closed projection; C-STAR-ALGEBRAS; OPEN PROJECTIONS; MULTIPLIERS; IDEALS;

D O I：

10.1016/j.jfa.2012.11.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We make several contributions to our recent program investigating structural properties of algebras of operators on a Hilbert space. For example, we make substantial contributions to the noncommutative peak interpolation program begun by Hay and the first author, Hay and Neal. Another sample result: an operator algebra has a contractive approximate identity iff the linear span of the elements with positive real part is dense. We also extend the theory of compact projections to the most general case. Despite the title, our algebras are often allowed to have no approximate identity. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：1049 / 1067

页数：19

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