On absolute summability for double triangle matrices
Mathematica Slovaca, vol.60, no.4, pp.495-506, 2010 (SCI-Expanded, Scopus)
- 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.