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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2504.11646 |
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| _version_ | 1866908321852686336 |
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| author | Ivanov, Nikolai V. Prokhorova, Marina |
| author_facet | Ivanov, Nikolai V. Prokhorova, Marina |
| contents | By a theorem of Dixmier-Douady the unitary group of an infinite-dimensional separable Hilbert space $H$ in the strong operator topology is contractible. The Dixmier-Douady proof is based on an explicit construction of families of subspaces and operators in $H$ with rather special properties. Unfortunately, this proof leaves hidden the geometric meaning of the theorem. The first goal of this note is to give a direct geometric proof of this theorem. The second goal is to provide a geometic analogue of Dixmier-Douady construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11646 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The unitary group in the strong topology and a construction of Dixmier-Douady Ivanov, Nikolai V. Prokhorova, Marina Functional Analysis Differential Geometry 47D03, 57S05 (Primary) 19K56, 46L80, 47A99 (Secondary) By a theorem of Dixmier-Douady the unitary group of an infinite-dimensional separable Hilbert space $H$ in the strong operator topology is contractible. The Dixmier-Douady proof is based on an explicit construction of families of subspaces and operators in $H$ with rather special properties. Unfortunately, this proof leaves hidden the geometric meaning of the theorem. The first goal of this note is to give a direct geometric proof of this theorem. The second goal is to provide a geometic analogue of Dixmier-Douady construction. |
| title | The unitary group in the strong topology and a construction of Dixmier-Douady |
| topic | Functional Analysis Differential Geometry 47D03, 57S05 (Primary) 19K56, 46L80, 47A99 (Secondary) |
| url | https://arxiv.org/abs/2504.11646 |