Restricting operators to thick Hilbert C*-submodules
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916195326754816 |
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| author | Manuilov, V. |
| author_facet | Manuilov, V. |
| contents | Given an essential ideal $J\subset A$ of a C*-algebra $A$, and a Hilbert C*-module $M$ over $A$, we place $M$ between two other Hilbert C*-modules over $A$, $M_J\subset M\subset M^J$, in such a way that each submodule here is thick, i.e. its orthogonal conmplement in the greater module is trivial. We introduce the class $\mathbb B_J(M)$ of $J$-adjointable operators on a Hilbert C*-module $M$ over $A$, and prove that this class isometrically embeds into the C*-algebras of all adjointable operators both of $M_J$ and of $M^J$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04185 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Restricting operators to thick Hilbert C*-submodules Manuilov, V. Operator Algebras Given an essential ideal $J\subset A$ of a C*-algebra $A$, and a Hilbert C*-module $M$ over $A$, we place $M$ between two other Hilbert C*-modules over $A$, $M_J\subset M\subset M^J$, in such a way that each submodule here is thick, i.e. its orthogonal conmplement in the greater module is trivial. We introduce the class $\mathbb B_J(M)$ of $J$-adjointable operators on a Hilbert C*-module $M$ over $A$, and prove that this class isometrically embeds into the C*-algebras of all adjointable operators both of $M_J$ and of $M^J$. |
| title | Restricting operators to thick Hilbert C*-submodules |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2404.04185 |