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

BİŞGİN M. C.

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, vol.0, no.0, 2020 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 0 Issue: 0
  • Publication Date: 2020
  • Doi Number: 10.2478/aupcsm-2020-0012
  • Journal Name: Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
  • Journal Indexes: Emerging Sources Citation Index (ESCI), zbMATH, Directory of Open Access Journals
  • Keywords: matrix domain, Schauder basis, beta- and gamma-duals, Banach Limits, almost convergence and matrix classes, INFINITE MATRICES
  • Recep Tayyip Erdoğan University Affiliated: Yes

Abstract

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.