Almost convergent sequence spaces derived by the domain of quadruple band matrix

Bişgin M. C.

ANNALES UNIVERSITATIS PAEDAGOGICAE CRACOVIENSIS. STUDIA MATHEMATICA, cilt.0, sa.0, 2020 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 0 Sayı: 0
  • Basım Tarihi: 2020
  • Doi Numarası: 10.2478/aupcsm-2020-0012
  • Dergi Adı: ANNALES UNIVERSITATIS PAEDAGOGICAE CRACOVIENSIS. STUDIA MATHEMATICA
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: matrix domain, Schauder basis, beta- and gamma-duals, Banach Limits, almost convergence and matrix classes, INFINITE MATRICES
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

In this work, we construct the sequence spaces f(Q(r, s, t, u)), f(0)(Q(r, s, t, u)) and fs(Q(r, s, t, u)), where Q(r, s, t, u) is quadruple band matrix which generalizes the matrices Delta(3), B(r, s, t), Delta(2), B(r, s) and Delta, where Delta(3), B(r, s, t), Delta(2), B(r, s) and Delta are called third order difference, triple band, second order difference, double band and difference matrix, respectively. Also, we prove that these spaces are BK-spaces and are linearly isomorphic to the sequence spaces f, f(0) and f(s), respectively. Moreover, we give the Schauder basis and beta, gamma-duals of those spaces. Lastly, we characterize some matrix classes related to those spaces.