On some locally convex FK spaces

Creative Commons License

Leonetti P., ORHAN C.

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

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 322
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1016/j.topol.2022.108327
  • Dergi Adı: TOPOLOGY AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Anahtar Kelimeler: Locally convex FK space, Ideal convergence, Tall ideal, Summability, IDEALS
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Ankara Üniversitesi Adresli: Evet

Özet

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.