1Department of Mathematics, Semnan University, Semnan, Iran
2Faculty 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∗).