The buck-pollard property for p-Cesàro matrices

Orhan C., Tas E., YURDAKADİM T.

Numerical Functional Analysis and Optimization, vol.33, no.2, pp.190-196, 2012 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 2
  • Publication Date: 2012
  • Doi Number: 10.1080/01630563.2011.597916
  • Journal Name: Numerical Functional Analysis and Optimization
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.190-196
  • Keywords: Borel property, Buck-Pollard property, Cesàro operator, Rademacher function, Summability of subsequences
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

Establishing a one-to-one correspondence between the interval (0, 1] and the collection of all subsequences of a given sequence {s n}, Buck and Pollard proved that {s n is (C, 1)-summable if almost all of subsequences are, but not conversely. In this article, we consider the analogous questions for the p-Cesro matrices. We show, for example, that if p>1/2 then a bounded sequence is C p-summable if and only if almost all of its subsequences are C p-summable. Copyright © 2012 Taylor and Francis Group, LLC.