International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 55, Pages 2963-2969

The structure of a subclass of amenable banach algebras

R. El Harti

Faculty of Sciences and Techniques (FST), University Hassan I-Settat, BP 577, Settat 2600, Morocco

Received 8 January 2004

Copyright © 2004 R. El Harti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.