A new uniform structure for Hilbert C^*-modules

2024/02/28 by D. V. Fufaev, Fufaev, Denis, Evgenij Troitsky +1 · 1 citation
Mathematics · #Holomorphic and Operator Theory #Advanced Operator Algebra Research #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2402.18261

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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