Matrix mappings and norms on the absolute Cesaro and weighted spaces

Abstract

In this paper, for alpha > -1 and k >= 1; we characterize the classes of all infinite matrices (vertical bar C alpha vertical bar(k), vertical bar(N) over bar (u)(p)vertical bar), (vertical bar C-alpha vertical bar, vertical bar(N) over bar (u)(p)vertical bar(k), vertical bar C-alpha vertical bar and (vertical bar(N) over bar (u)(p)vertical bar, vertical bar C-alpha vertical bar(k)), where the absolute spaces vertical bar C-alpha vertical bar(k) vertical bar(N) over bar (u)(p)vertical bar(k) are defined by Sarlgol [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 Sarigol [22] are generalized.