A lexicographical order induced by Schauder bases

Authors : Neset TAN

Pages : 511-515

Doi:10.15672/hujms.659795

View : 12 | Download : 5

Publication Date : 2021-04-11

Article Type : Research Paper

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 insert ignore into journalissuearticles values(cone); sense.
Keywords : total order, cone, Schauder basis