Homological Properties of Some Types of Generalized Matrix Banach Algebras

Let G be a generalized matrix Banach algebra associated with a Morita context (A, B, M, N, , ). In this paper, we investigate biprojectivity and biflatness of G, under certain conditions. Indeed, we obtain a biprojective (resp. biflat) generalized matrix Banach algebra such that M = 0 and N = 0. Moreover, we give a sufficient condition for biprojectivity and biflatness of G, in the case where A = N = 0. Using this fact, we obtain some results about homological properties of bi-amalgamated Banach algebras. As an application, we answer some recent open questions.