A new uniform structure for Hilbert $C^*$-modules
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909122756083712 |
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| author | Fufaev, Denis Troitsky, Evgenij |
| author_facet | Fufaev, Denis Troitsky, Evgenij |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18261 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new uniform structure for Hilbert $C^*$-modules Fufaev, Denis Troitsky, Evgenij Operator Algebras Functional Analysis 46L08, 47B10, 47L80, 54E15 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. |
| title | A new uniform structure for Hilbert $C^*$-modules |
| topic | Operator Algebras Functional Analysis 46L08, 47B10, 47L80, 54E15 |
| url | https://arxiv.org/abs/2402.18261 |