Banach function spaces done right
arXiv:2307.01173 · doi:10.1016/j.indag.2023.11.004
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.
arXiv comment19 pages, to appear in Indagationes Mathematicae
References in corpus (1)
Cited by in corpus (7)
- On the properties of quasi-Banach function spaces
- A discrete framework for the interpolation of Banach spaces
- Extrapolation of compactness on Banach function spaces
- A lattice approach to matrix weights
- On the properties of rearrangement-invariant quasi-Banach function spaces
- Strongly Kreiss Bounded Operators in UMD Banach Spaces
- Absolute continuity of the (quasi)norm in rearrangement-invariant spaces