SUFFICIENT CONDITIONS FOR FACTORABLE MATRICES TO BE BOUNDED OPERATORS ON A(k)

Savas E., Şevli H., RHOADES B. E.

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, vol.39, no.2, pp.633-644, 2009 (SCI-Expanded) identifier identifier

  • 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
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

A factorable matrix A is a lower triangular matrix with entries a(nk) = a(n)b(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 is an element of B(A(k)). As corollaries we obtain sufficient conditions for the discrete Cesdro, terraced, and P-Cesaro matrices defined by Rhaly, to be in B(A(k)).