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arXiv · 2402.18261

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

Denis Fufaev·Evgenij Troitsky
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Abstract

We introduce and study some new uniform structures for Hilbert $C^*$-modules over an 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.

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BibTeXRIS

Denis Fufaev, Evgenij Troitsky. 2024-02-28. A new uniform structure for Hilbert $C^*$-modules. https://arxiv.org/abs/2402.18261

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