2024/12/17 by Fernando Abadie, Abadie, Fernando · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2412.12446
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.