Compact matrix operators on Banach space of absolutely k-summable series

Abstract

In a more recent paper [23], Banach spaces of absolutely k-summable series vertical bar T-phi vertical bar(k) have been introduced and studied by Sarigol and Agarwal. In this paper, we characterize matrix and compact operators from the space vertical bar T-phi vertical bar(k) to the classical spaces c(0), c and l(infinity), by determining identities or estimates for operator norms and the Hausdorff measure of noncompactness.