Banach function spaces done right
Emiel Lorist, Zoe Nieraeth
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.
Topics & Concepts
MathematicsBanach spaceInterpolation spaceFunction spaceBanach manifoldFunction (biology)Lp spaceInfinite-dimensional vector functionPure mathematicsEberlein–Šmulian theoremSpace (punctuation)Functional analysisComputer scienceBiochemistryEvolutionary biologyGeneBiologyChemistryOperating systemAdvanced Banach Space TheoryAdvanced Harmonic Analysis ResearchHolomorphic and Operator Theory