A lexicographical order induced by Schauder bases

Year 2021, Volume: 50 Issue: 2, 511 - 515, 11.04.2021

Neset Tan

https://doi.org/10.15672/hujms.659795

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

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