Characterization of absolute summability factors

Abstract

By (A, B) we denote the set of all sequences ? = (?n) such that ?an?n is summable B, whenever ?an is summable A, where A and B are summability methods. In the present paper we characterize the sets (|N¯, pn|, |N¯, qn|k) and (|N¯, pn|k, |N¯, qn|), 1 ? k < ?, using functional analytic techniques, and also extend some known results. © 1995 Academic Press, Inc.