On some classical properties of normed spaces via generalized vector valued almost convergence

Karakuş M., Başar F.

Mathematica Slovaca, vol.72, no.6, pp.1551-1566, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 72 Issue: 6
  • Publication Date: 2022
  • Doi Number: 10.1515/ms-2022-0106
  • Journal Name: Mathematica Slovaca
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.1551-1566
  • Keywords: completeness, reexivity, Schur and Grothendieck properties, Summability methods
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

© 2022 Mathematical Institute Slovak Academy of Sciences.Recently, the authors interested some new problems on multiplier spaces of Lorentz' almost convergence and fλ-convergence as a generalization of almost convergence. fλ-convergence is firstly introduced by Karakuş and Başar, and used for some new characterizations of completeness and barrelledness of the spaces through weakly unconditionally Cauchy series in a normed space X and its continuous dual X∗. In the present paper, we deal with fλ-convergence to have some inclusion relations between the vector valued spaces obtained from this type convergence and corresponding classical sequence spaces, and to give new characterizations of some classical properties like completeness, reflexivity, Schur property and Grothendieck property of normed spaces. By the way, we give a characterization of finite-dimensional normed spaces.