A new uniform structure for Hilbert C∗-modules

被引：0

作者：

Fufaev, Denis ^{[1
]}

Troitsky, Evgenij ^{[1
]}

机构：

[1] Lomonosov Moscow State Univ, Moscow Ctr Fundamental & Appl Math, Dept Mech & Math, Moscow 119991, Russia

来源：

ANNALS OF FUNCTIONAL ANALYSIS | 2024年 / 15卷 / 03期

基金：

俄罗斯科学基金会;

关键词：

Hilbert C-& lowast; -module; Uniform structure; Totally bounded set; Multiplier; Compact operator; A-compact operator; C-ASTERISK-MODULES; COMPACT-OPERATORS; FRAMES;

D O I：

10.1007/s43034-024-00368-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce and study some new uniform structures for Hilbert C-& lowast;-modules over a C-& lowast;-algebra A. In particular, we prove that in some cases they have the same totally bounded sets. To define one of them, we introduce a new class of A-functionals: locally adjointable functionals, which have interesting properties in this context and seem to be of independent interest. A relation between these uniform structures and the theory of A-compact operators is established.

引用

页数：16

共 25 条

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