Necessary Conditions for Inclusion Relations for Absolute Summability

Abstract

Let 1 < k less than or equal to s < infinity. In this paper we obtain necessary conditions for a series summable \A\(k) to imply that the series is summable \B\(s), where A and B are two lower triangular matrices. We also obtain several corollaries. (C) 2003 Elsevier Inc. All rights reserved.