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 lefta-module and right b-module. we consider generalized derivations associatewith hochschild 2-cocycles on triangular banach algebra t (relatedto a, b and m). we characterize this new version of generalizedderivations on triangular banach algebras and we obtain some resultsfor l1 ? direct summands of banach algebras.