Operator algebras and unitary representations of Polish groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913823265390592 |
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| author | Quiroga-Barranco, Raul |
| author_facet | Quiroga-Barranco, Raul |
| contents | We study the relationship between operator algebras, $C^*$ and von Neumann, acting on a Hilbert space and unitary representations of topological groups on the same space. We obtain certain correspondences between both these families of objects. In particular, we prove that the study of Abelian subalgebras of a norm-separable $C^*$-algebra can be, in many aspects, reduced to the study of unitary representations of Polish groups. It is shown that our techniques have applications to the construction and classification of Abelian subalgebras of operator $C^*$-algebras on separable Hilbert spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09601 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Operator algebras and unitary representations of Polish groups Quiroga-Barranco, Raul Operator Algebras Primary 46L10, Secondary 46L35 We study the relationship between operator algebras, $C^*$ and von Neumann, acting on a Hilbert space and unitary representations of topological groups on the same space. We obtain certain correspondences between both these families of objects. In particular, we prove that the study of Abelian subalgebras of a norm-separable $C^*$-algebra can be, in many aspects, reduced to the study of unitary representations of Polish groups. It is shown that our techniques have applications to the construction and classification of Abelian subalgebras of operator $C^*$-algebras on separable Hilbert spaces. |
| title | Operator algebras and unitary representations of Polish groups |
| topic | Operator Algebras Primary 46L10, Secondary 46L35 |
| url | https://arxiv.org/abs/2402.09601 |