Matrix mappings and norms on the absolute Cesàro and weighted spaces

Abstract

In this paper, for α > -1 and k ≥ 1, we characterize the classes of all infinite matrices (|C_α|_k, |N^u_p|), (|C_α|, |N^u_p|_k), (|N^u_p|_k, |C_α|) and (|N^u_p|_k, |C_α|_k), where the absolute spaces |C_α|_k and |N^u_p|_k are defined by Sarıgöl [22 - 24]. Also we obtain estimates for the norms of bounded linear operators corresponding to matrices in these classes. So not only some problems are solved but also some well known results of Mehdi [12], Mazhar [11], Mohapatra and Das [13] and Sarıgöl [22]
are generalized.

Mathematics Subject Classification (2010): 40C05, 40D25, 40F05, 46A45.

Keywords: Absolute summability, matrix operators, BK spaces, norms