(-1)-weak amenability of Unitized Banach Algebras

Abstract

 

 For a Banach algebra A, its second dual A'' is (-1)-weakly amenable

if A' is a Banach A''-bimodule and the first cohomology group of A'' with coefficients in A' is zero i.e. H1(A'',A') = {0}.

In this paper we give some conditions, under each of which A' is a Banach

A''-bimodule. We also investigate the relations between (-1)-weak amenability of A and A#, where A#is the unitization of A.