A lexicographical order induced by schauder bases

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Tan N. Ö.

Hacettepe Journal of Mathematics and Statistics, vol.50, no.2, pp.511-515, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.15672/hujms.659795
  • Journal Name: Hacettepe Journal of Mathematics and Statistics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.511-515
  • Keywords: Cone, Schauder basis, Total order
  • Uşak University Affiliated: Yes

Abstract

In this paper, we show that every Banach space with a Schauder basis can be seen as a totally ordered vector space. Indeed, this order can be considered as a lexicographical order since it is a generalization of lexicographical order in Rn. We also provide order structural properties of the order by approaching geometrical (cone) sense.