On absolute summability for double triangle matrices


Savas E., Sevli H.

MATHEMATICA SLOVACA, vol.60, no.4, pp.495-506, 2010 (SCI-Expanded) 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
  • Van Yüzüncü Yıl University Affiliated: No

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 A(k)(2); i.e., T is an element of B (A(k)(2)) for the sequence space A(k)(2) defined below. As special summability methods T we consider weighted mean and double Cesaro, (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.