Some new results related to compact matrix operators in the class ((ℓ p ) T , ℓ ∞)

Abstract

The main goal of this paper is to establish necessary and sufficient conditions for a matrix A ∈ ((lp)T, l∞), where T is an arbitrary triangle, 1 ≤ p ≤ ∞, to be a compact operator. In the past, only sufficient conditions were established in almost all of those cases, by using the Hausdorff measure of noncompactness. We improve those results by applying another method for the characterizations of compact linear operators between BK spaces.