Weak character amenability of Banach algebras

Abstract

In the present paper we first investigate the relations between weak character amenability of   and weak character amenability of , where  is the second dual algebra of  endowed with the first or second Arens product. Then we introduce and study the concept of weak -amenability of a Banach algebra , where , the character space of . We give some interesting examples and establish a characterization of weak -amenability. Moreover we prove some hereditary properties and investigate weak -amenability for  projective tensor product