Single and multi-valued Hilbert-bundle renormings
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915058460655616 |
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| author | Chirvasitu, Alexandru |
| author_facet | Chirvasitu, Alexandru |
| contents | We prove that subhomogeneous continuous Banach bundles over compact metrizable spaces are equivalent to Hilbert bundles, while examples show that the metrizability assumption cannot be dropped completely. This complements the parallel statement for homogeneous bundles without the metrizability assumption, and generalizes the analogous result to the effect that subhomogeneous $C^*$ bundles over compact metrizable spaces admit finite-index expectations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08094 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Single and multi-valued Hilbert-bundle renormings Chirvasitu, Alexandru Functional Analysis Category Theory General Topology Operator Algebras 46B03, 46M20, 54C65, 46C05, 52A21, 52A01, 54E35, 54B20 We prove that subhomogeneous continuous Banach bundles over compact metrizable spaces are equivalent to Hilbert bundles, while examples show that the metrizability assumption cannot be dropped completely. This complements the parallel statement for homogeneous bundles without the metrizability assumption, and generalizes the analogous result to the effect that subhomogeneous $C^*$ bundles over compact metrizable spaces admit finite-index expectations. |
| title | Single and multi-valued Hilbert-bundle renormings |
| topic | Functional Analysis Category Theory General Topology Operator Algebras 46B03, 46M20, 54C65, 46C05, 52A21, 52A01, 54E35, 54B20 |
| url | https://arxiv.org/abs/2412.08094 |