A lexicographical order induced by schauder bases
Hacettepe Journal of Mathematics and Statistics, vol.50, no.2, pp.511-515, 2021 (SCI-Expanded, Scopus, TRDizin)
- 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: total order, cone, Schauder basis
- Open Archive Collection: AVESIS Open Access Collection
- Usak 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.