Conditional expectations on Fell bundles
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929634161983488 |
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| author | Abadie, Fernando |
| author_facet | Abadie, Fernando |
| contents | We show that the existence of a continuous conditional expectation from a Fell bundle to a Fell subbundle implies that the full cross-sectional C*-algebra of the subbundle is contained in the full cross-sectional C*-algebra of the bundle, and moreover there exists a conditional expectation from the latter algebra to the former. A similar fact holds for the reduced cross-sectional C*-algebras. Besides, the subbundle is amenable whenever so is the bundle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12446 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conditional expectations on Fell bundles Abadie, Fernando Operator Algebras We show that the existence of a continuous conditional expectation from a Fell bundle to a Fell subbundle implies that the full cross-sectional C*-algebra of the subbundle is contained in the full cross-sectional C*-algebra of the bundle, and moreover there exists a conditional expectation from the latter algebra to the former. A similar fact holds for the reduced cross-sectional C*-algebras. Besides, the subbundle is amenable whenever so is the bundle. |
| title | Conditional expectations on Fell bundles |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2412.12446 |