On (Co)homology of triangular Banach algebras

Abstract

Abstract. Suppose that A and B are unital Banach algebras with units 1 A and 1 B , respectively, M is a unital Banach A, B-module, T = [Applying two nice long exact sequences related to A, B, T , X, X AA , X BB , X AB and X BA we establish some results on (co)homology of triangular Banach algebras. . Forrest and Marcoux also studied and directly computed some cohomology groups of triangular Banach algebras (see [2] and [3]). In this paper, after some preliminaries, we present two long exact sequences and apply them to give some significant isomorphisms and vanishing theorems.