On some locally convex FK spaces

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Leonetti P., ORHAN C.

TOPOLOGY AND ITS APPLICATIONS, vol.322, 2022 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 322
  • Publication Date: 2022
  • Doi Number: 10.1016/j.topol.2022.108327
  • Journal Name: TOPOLOGY AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Keywords: Locally convex FK space, Ideal convergence, Tall ideal, Summability, IDEALS
  • Open Archive Collection: AVESIS Open Access Collection
  • Ankara University Affiliated: Yes

Abstract

We provide necessary and/or sufficient conditions on vector spaces V of real sequences to be a Frechet space such that each coordinate map is continuous, that is, to be a locally convex FK space. In particular, we show that if c00(I) subset of V subset of $infinity(I) for some ideal I on w, then V is a locally convex FK space if and only if there exists an infinite set S subset of w for which every infinite subset does not belong to I.(c) 2022 Elsevier B.V. All rights reserved.