A generalization on character Connes-amenability

Abstract

In the present paper, the concepts of left '-approximate Connes-amenability and
left character approximate Connes-amenability of a dual Banach algebra A that ' is a !-
continuous homomorphism from A to C, are introduced. We characterize left '-approximate
Connes-amenability of A in terms of certain derivations and study some hereditary properties
for such Banach algebras. Finally, by means of some examples the distinction between these
new notions and approximate Connes-amenability [5] or left character Connes-amenability
[21] of dual Banach algebras are shown.