A new uniform structure for Hilbert $C^*$-modules

IF 1.2 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2024-06-03 DOI:10.1007/s43034-024-00368-3

Denis Fufaev, Evgenij Troitsky

引用次数: 0

Abstract

We introduce and study some new uniform structures for Hilbert $C^*$-modules over a $C^*$-algebra $\mathcal {A}.$ 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 $\mathcal {A}$-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 $\mathcal {A}$-compact operators is established.

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希尔伯特 $$C^*$$ 模块的新统一结构

我们引入并研究了在$C^*$-代数$\mathcal {A}.$上的希尔伯特$C^*$-模块的一些新的统一结构，特别是，我们证明了在某些情况下它们具有相同的完全有界集。为了定义它们中的一个，我们引入了一类新的（\mathcal {A}\）-函数：局部可邻接函数，它们在这种情况下具有有趣的性质，似乎具有独立的意义。我们建立了这些统一结构与（\mathcal {A}\）紧凑算子理论之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Functional Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory. Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.

A new uniform structure for Hilbert \(C^*\)-modules

Abstract