CONNES-AMENABILITY OF TRIANGULAR BANACH ALGEBRAS

Let A and B be unital Banach algebras and M be a Banach (A,B)-module. Then T =(A M 0 B) becomes a triangular Banach algebra when equipped with the Banach space norm ||T|| = ||a|| A + ||m|| M + ||b|| B. When A and B are dual Banach algebras, we characterize Connes-amenability of T in terms of Connes-amenability of A and B and their action on M.