Banach function spaces done right
Functional Analysis
2024-05-31 v2 Classical Analysis and ODEs
Abstract
In this survey, we discuss the definition of a (quasi-)Banach function space. We advertise the original definition by Zaanen and Luxemburg, which does not have various issues introduced by other, subsequent definitions. Moreover, we prove versions of well-known basic properties of Banach function spaces in the setting of quasi-Banach function spaces.
Keywords
Cite
@article{arxiv.2307.01173,
title = {Banach function spaces done right},
author = {Emiel Lorist and Zoe Nieraeth},
journal= {arXiv preprint arXiv:2307.01173},
year = {2024}
}
Comments
19 pages, to appear in Indagationes Mathematicae