Hausdorff measure of noncompactness of certain matrix operators on absolute norlund spaces

Abstract

The absolute Norlund spaces vertical bar N-p(u)vertical bar(k), k >= 1, have more recently been introduced and studied by Hazar and Sargol [On absolute Norlund spaces and matrix operators, Acta Math. Sin. (Engl. Ser.), 34 (5) (2018), 812-826]. In the present paper, we characterize the classes of infinite matrix and compact operators transforming from vertical bar N-p(u)vertical bar(k) into X and obtain some identities or estimates for the Hausdorff measures of noncompactness, where X is one of the spaces l(infinity), c and c(0).