The Measure Algebra of a Locally Compact Group

Abstract

<p> Let G be a locally compact group (= locally compact Hausdorff topological group). By the measure algebra of G we mean the Banach *-algebra M(G) of bounded regular Borel measures on G. The major results of this work are a structure theorem for norm decreasing isomorphisms of measure algebras, and a characterization of those Banach algebras which are isometric and isomorphic to the measure algebra of some locally compact group. We also obtain some results on subalgebras of M(G) and on representations of G.</p>