ON MODULE EXTENSION BANACH ALGEBRAS

Let A be a Banach algebra and X be a Banach A- bimodule. Then S = A X, the l 1 -direct sum of A and X becomes a module extension Banach algebra when equipped with the algebra product (a;x):(a ' ;x ' ) = (aa ' ;ax ' +xa ' ): In this paper, we investigate biatness and biprojectivity for these Banach algebras. We also discuss on automatic continuity of derivations on S = A A.