- Hacettepe Journal of Mathematics and Statistics
- Vol: 50 Issue: 2
- A lexicographical order induced by Schauder bases
A lexicographical order induced by Schauder bases
Authors : Neset Tan
Pages : 511-515
Doi:10.15672/hujms.659795
View : 11 | Download : 6
Publication Date : 2021-04-11
Article Type : Research
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 $\mathbb{R}^{n}.$ We also provide order structural properties of the order by approaching geometrical (cone) sense.Keywords : total order, cone, Schauder basis