In this paper, we show that the class of I I matrices with nite `p-norm is always pseudo-amenable, where 1 p 2: As an application, for the case p = 1, we give some applications for semigroup algebras. Also we study approximate homological notions for the class of upper triangular matrix algebras with respect to the Esslamzadeh-Munn algebras. Keywords: matrix algebras, pseudo-amenability, approximate biprojectivity
