Banach function spaces done right

Review (2024)

Authors

E. Lorist Analysis - EEMCS
Zoe Nieraeth BCAM Basque Center for Applied Mathematics
Research Group
Analysis (EEMCS) (TU Delft)
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Published Date

2024

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

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.