VECTOR VALUED CLOSED SUBSPACES AND CHARACTERIZATIONS OF NORMED SPACES THROUGH (J'-SUMMABILITY


Karakuş M., Başar F.

Indian Journal of Mathematics, cilt.66, sa.1, ss.85-105, 2024 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 66 Sayı: 1
  • Basım Tarihi: 2024
  • Dergi Adı: Indian Journal of Mathematics
  • Derginin Tarandığı İndeksler: Scopus, zbMATH
  • Sayfa Sayıları: ss.85-105
  • Anahtar Kelimeler: completeness, reflexivity, Schur and Grothendieck properties, summability methods
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

Aizpuru and Nicasio-Llach [1] introduced the spaces of vector valued sequences defined by statistical convergence and beside of some new characterizations like completeness, reflexivity and Shur properties of normed spaces, they also obtained a new version of Antosik-Swartz basic matrix theorem. Aizpuru et al. [21 and Kama [131 studied these properties in terms of vector valued ahnost convergence and I-statistical convergence, respectively. Recently, the authors gave some similar results on normed spaces by using a generalization of vector valued almost convergence, [17]. ill the present paper, we essentially deal with invariant means (a-summability) to have some new vector valued closed subspaces of loo(X) and bs(X), and to get some new characterizations of completeness, reflexivity, Schur and Grothendieck properties of nonned spaces. We also give a new characterization of finite dimensionality of normed spaces.