Characterization of Generalized Derivations Associate with Hochschild 2-Cocycles on Triangular Banach Algebras

Let A and B be unital Banach algebras and M be a left A-module and right B-module. We consider generalized derivations associate with Hochschild 2-cocycles on triangular Banach algebra T (related to A, B and M). We characterize this new version of generalized derivations on triangular Banach algebras and we obtain some results for l1 ? direct summands of Banach algebras.