Norms and compactness of operators on absolute weighted mean summable series

Abstract

In a recent paper we characterized the classes of triangular matrix transformations mapping from the spaces |N¯p| and |N¯? p|k into the spaces |N¯? q|k and |N¯q|, respectively, where the spaces |N¯? p|k, k?1, series summable by absolute summability method. In the present paper we show that each element of these classes corresponds to a bounded linear operator, and determine exactly or estimate their norms and those in some well known classes. Also, we characterize compact operators in these classes by using Hausdorff measure of noncompactness. © 2016, University of Kuwait. All rights reserved.