On absolute summability for double triangle matrices

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Savaş E., Şevli H.

Mathematica Slovaca, vol.60, no.4, pp.495-506, 2010 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 60 Issue: 4
  • Publication Date: 2010
  • Doi Number: 10.2478/s12175-010-0028-4
  • Journal Name: Mathematica Slovaca
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.495-506
  • Keywords: bounded operator, double sequence space, triangular matrices, A(k) spaces, weighted mean methods
  • Open Archive Collection: AVESIS Open Access Collection
  • İstanbul Ticaret University Affiliated: Yes

Abstract

A lower triangular infinite matrix is called a triangle if there are no zeros on the principal diagonal. The main result of this paper gives a minimal set of sufficient conditions for a double triangle T to be a bounded operator on Ak2; i. e., T ∈ B (Ak2) for the sequence space Ak2 defined below. As special summability methods T we consider weighted mean and double Cesàro, (C, 1, 1), methods. As a corollary we obtain necessary and sufficient conditions for a double triangle T to be a bounded operator on the space BV of double sequences of bounded variation. © 2010 Versita Warsaw and Springer-Verlag Wien.