Banach algebra amenability and group algebras

Abstract

The primary purpose of the research presented in this thesis is to investigate the extent to which amenability in Banach algebras is reliant on amenability in locally compact groups. One of the first results proven on amenability in Banach algebras was the equivalence of the amenability of a locally compact group G with the amenability of its group algebra L¹( G). Other instances of amenability in Banach algebras can then be demonstrated by the use of certain constructions which preserve amenability.