On absolute summability for double triangle matrices

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Savaş E., Şevli H.

Mathematica Slovaca, cilt.60, sa.4, ss.495-506, 2010 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 60 Sayı: 4
  • Basım Tarihi: 2010
  • Doi Numarası: 10.2478/s12175-010-0028-4
  • Dergi Adı: Mathematica Slovaca
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.495-506
  • Anahtar Kelimeler: Ak spaces, Bounded operator, Double sequence space, Triangular matrices, Weighted mean methods
  • Uşak Üniversitesi Adresli: Hayır

Özet

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.