ON MODULE CONNES AMENABILITY FOR MODULE EXTENSION OF DUAL BANACH ALGEBRAS

Let A be a dual Banach algebra with predual A∗ and U is a Banach algebra such that A is a Banach U-bimodule via compatible actions. Let Ω be a normal Banach A-bimodule with predual Ω∗. In this paper, we develop the notions of module Connes amenability for module (ψU , 0)-Connes amenability of module extension of Banach algebra A ⊕ Ω, where ψU is a bounded module algebraic homomorphism from A into itself.