On bimodule Connes amenability of certain Banach algebras

Abstract

Let A = (A) and B = (B) be dual Banach
algebras and U be a Banach algebra. Let
Ω = (Ω) be a normal Banach A-bimodule.
In this paper, we investigate the notion of U-
bimodule φAU

  B
U -Connes amenability for
Ab
B, where φAU
: A ! A and  B
U : B ! B
are w-continuous homomorphisms. Also, we
characterize the U-bimodule ( B
U ; 0)-Connes
amenability of the module extension of dual
Banach algebra A Ω.