Document Type: Review Paper


1 Department of Mathematics, Semnan University, Semnan, Iran

2 Faculty of Engineering- East Guilan, University of Guilan, Rudsar, Iran


The purpose of this article is to develop the notions of amenability
for vector valued group algebras. We prove that L1(G, A) is approximately
weakly amenable where A is a unital separable Banach algebra. We give
necessary and sufficient conditions for the existence of a left invariant mean
on L∞(G, A∗), LUC(G, A∗), WAP(G, A∗) and C0(G, A∗).