International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 53-56, Pages 2963-2969
doi:10.1155/S0161171204401069

The structure of a subclass of amenable Banach algebras

Abstract

We give sufficient conditions that allow contractible (resp., reflexive amenable) Banach algebras to be finite-dimensional and semisimple algebras. Moreover, we show that any contractible (resp., reflexive amenable) Banach algebra in which every maximal left ideal has a Banach space complement is indeed a direct sum of finitely many full matrix algebras. Finally, we characterize Hermitian *-algebras that are contractible.