Mathematical Proceedings of the Cambridge Philosophical Society

Symmetric amenability and Lie derivations

J. ALAMINOS a1 1 , M. MATHIEU a2 and A. R. VILLENA a1 2
a1 Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain. e-mail:
a2 Department of Pure Mathematics, Queen's University Belfast, Belfast BT 7 1NN, Northern Ireland. e-mail:

Article author query
alaminos j   [Google Scholar] 
mathieu m   [Google Scholar] 
villena ar   [Google Scholar] 


We prove that every Lie derivation on a symmetrically amenable semisimple Banach algebra can be uniquely decomposed into the sum of a derivation and a centre-valued trace.

(Received January 5 2002)
(Revised February 14 2003)


1 Supported by MCYT Grant BFM2000-1467.

2 Supported by MCYT Grant PB1998-1358.