Products and Factors of Banach function spaces
Anton R. Schep
TL;DR
This paper investigates the properties of pointwise product spaces of Banach function spaces, focusing on convexity conditions and the characterization of multiplication operator spaces.
Contribution
It provides new conditions under which the pointwise product of Banach function spaces is convex and characterizes when the multiplication operator space equals one of the original spaces.
Findings
Conditions for convexity of product spaces
Characterization of multiplication operator spaces
Insights into the structure of Banach function space products
Abstract
Given two Banach function spaces we study the pointwise product space E.F, especially for the case that the pointwise product of their unit balls is again convex. We then give conditions on when the pointwise product E . M(E, F)=F, where M(E,F) denotes the space of multiplication operators from E into F.
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Taxonomy
TopicsAdvanced Banach Space Theory