Extension of Mazhar's theorem on summability factors

Abstract

By (X,Y) we denote the set of all sequences such ? that ?an?, is summable Y whenever ? an is summable , where X and Y are summability methods. In this paper we characterize the set (|C,?|k'|N,pn|) for K >1,? >-1 and arbitrary positive sequences (pn) using functional analytic techniques, and so extend some known results.