BIFLATNESS AND BIPROJECTIVITY OF TRIANGULAR BANACH ALGEBRAS

Let A and B be Banach algebras and M be a Banach(A,B)-module. Then, T = A M0 B equipped with the usual2 × 2 matrix operations, obvious internal module actions and theBanach space norm k a m0 b = α A + kmkM + = b B is atriangular Banach algebra. We show that T is biflat if and only ifA and B are biflat and M = 0, where M is an essential (A,B)-module, that is, AM = M = MB. A similar result is obtained on biprojectivity.