Linearization and compactness
Volume 191 / 2009
Studia Mathematica 191 (2009), 181-200
MSC: 46E10, 46E50, 47B07.
DOI: 10.4064/sm191-2-6
Abstract
This paper is devoted to several questions concerning linearizations of function spaces. We first consider the relation between linearizations of a given space when it is viewed as a function space over different domains. Then we study the problem of characterizing when a Banach function space admits a Banach linearization in a natural way. Finally, we consider the relevance of compactness properties in linearizations, more precisely, the relation between different compactness properties of a mapping, and compactness of its associated linear operator.
