Strongly embedded subspaces of p-convex Banach function spaces

Abstract

Let be a p-convex () order continuous Banach function space over a positive finite measure . We characterize the subspaces of which can be found simultaneously in and a suitable space, where is a positive finite measure related to the representation of as an space of a vector measure . We provide in this way new tools to analyze the strict singularity of the inclusion of in such an space. No rearrangement invariant type restrictions on are required.