In the present paper, we study approximate biprojectivity and weak approximate biprojectivity of ‘1-Munn Banach algebras when the related sandwich matrix is regular over Inv(A). In fact, we show that a ‘1-Munn Banach algebra with the regular sandwich matrix over Inv(A) is approximately biprojective (weak approximately biprojective) if and only if A is approximately biprojective (weak approximately biprojective), respectively. We also study approximate biprojectivity of upper triangular Banach algebra when the associated sandwich matrix with elements in Inv(A) is invertible. Finally, we apply our results to Rees semigroup algebras.
