ON CERTAIN PRODUCT OF BANACH MODULES

Let A and B be Banach algebras and let B be an algebraic Banach Abimodule. Then the ℓ1direct sum A B equipped with the multiplication (a1; b1)(a2; b2) = (a1a2; a1b2+b1a2+b1b2); (a1; a2 2 A; b1; b2 2 B) is a Banach algebra denoted by A ▷◁ B. Module extension algebras, Lau product and also the direct sum of Banach algebras are the main examples satisfying this framework. We obtain characteriza- tions of bounded approximate identities, spectrum, and topological center of this product. This provides a unied approach for obtain- ing some known results of both module extensions and Lau product of Banach algebras