On Symmetry of $L^1$-Algebras Associated to Fell Bundles

Abstract

To every Fell bundle C over a locally compact group G one associates a Banach * -algebra L 1 (G | C ) . We prove that it is symmetric whenever G with the discrete topology is rigidly symmetric. A very general example is the Fell bundle associated to a twisted partial action of G on a C * -algebra A . This generalizes the known case of a global action without a twist.