Conditional expectations on Fell bundles
Operator Algebras
2024-12-18 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2412.12446,
title = {Conditional expectations on Fell bundles},
author = {Fernando Abadie},
journal= {arXiv preprint arXiv:2412.12446},
year = {2024}
}
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17 pages