Approximate Biprojectivity of ℓ1-Munn Banach Algebras

Abstract

In the present paper, we study the approximate biprojectivity and weak approximate biprojectivity of ℓ1-Munn Banach algebras when the related sandwich matrix is regular over InvA. In fact, we show that a ℓ1-Munn Banach algebra with the regular sandwich matrix over InvA 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 InvA is invertible. Finally, we apply our results to Rees semigroup algebras.