Sufficient conditions for factorable matrices to be bounded operators on a k

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Savaş E., Şevli H., Rhoades B.

Rocky Mountain Journal of Mathematics, vol.39, no.2, pp.633-644, 2009 (SCI-Expanded, Scopus)

• Publication Type: Article / Article
• Volume: 39 Issue: 2
• Publication Date: 2009
• Doi Number: 10.1216/rmj-2009-39-2-633
• Journal Name: Rocky Mountain Journal of Mathematics
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.633-644
• Keywords: Bounded operator, factorable matrices, Rhaly matrices, A(k) spaces
• Open Archive Collection: AVESIS Open Access Collection
• İstanbul Ticaret University Affiliated: Yes

Abstract

A factorable matrix A is a lower triangular matrix with entries a nk = a nb k. The sequence space A k is defined in (2). In this paper we determine sufficient conditions for a nonnegative factorable matrix A to be a bounded operator on A k, i.e., A ∈ B(A k)- As corollaries we obtain sufficient conditions for the discrete Cesáro, terraced, and p-Cesáro matrices defined by Rhaly, to be in B(A k) Copyright © 2009 Rocky Mountain Mathematics Consortium.