Locally adjointable operators on Hilbert $C^*$-modules
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910351054864384 |
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| author | Fufaev, Denis Troitsky, Evgenij |
| author_facet | Fufaev, Denis Troitsky, Evgenij |
| contents | In the theory of Hilbert $C^*$-modules over a $C^*$-algebra $A$ (in contrast with the theory of Hilbert spaces) not each bounded operator ($A$-homomorphism) admits an adjoint. The interplay between the sets of adjointable and non-adjointable operators plays a very important role in the theory. We study an intermediate notion of locally adjointable operator $F:M \to N$, i.e. such an operator that $F\circ g$ is adjointable for any adjointable $g: A \to M$. We have introduced this notion recently and it has demonstrated its usefulness in the context of theory of uniform structures on Hilbert $C^*$-modules. In the present paper we obtain an explicit description of locally adjointable operators in important cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01448 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Locally adjointable operators on Hilbert $C^*$-modules Fufaev, Denis Troitsky, Evgenij Operator Algebras Functional Analysis 46L08, 47B10, 47L80, 54E15 In the theory of Hilbert $C^*$-modules over a $C^*$-algebra $A$ (in contrast with the theory of Hilbert spaces) not each bounded operator ($A$-homomorphism) admits an adjoint. The interplay between the sets of adjointable and non-adjointable operators plays a very important role in the theory. We study an intermediate notion of locally adjointable operator $F:M \to N$, i.e. such an operator that $F\circ g$ is adjointable for any adjointable $g: A \to M$. We have introduced this notion recently and it has demonstrated its usefulness in the context of theory of uniform structures on Hilbert $C^*$-modules. In the present paper we obtain an explicit description of locally adjointable operators in important cases. |
| title | Locally adjointable operators on Hilbert $C^*$-modules |
| topic | Operator Algebras Functional Analysis 46L08, 47B10, 47L80, 54E15 |
| url | https://arxiv.org/abs/2403.01448 |