On the equivalence of twisted group algebras and Banach *-algebraic bundles

Abstract

The relationship between twisted group algebras and Banach ∗ ^\ast -algebraic bundles is investigated. Informally stated, the results are that bundles with Borel cross sections correspond to twisted group algebras, and “locally continuous” twisted group algebras correspond to bundles. In the separable case, these results combine to give a complete correspondence between the bundles and the “locally continuous” algebras.