Compact and weakly compact disjointness preserving operators on spaces of differentiable functions

TL;DR

This paper characterizes compact and weakly compact operators that preserve disjointness between spaces of Banach space-valued differentiable functions, advancing understanding of their structure and properties.

Contribution

It provides a complete characterization of compact and weakly compact disjointness preserving operators on Banach space-valued differentiable function spaces.

Findings

Characterization of compact disjointness preserving operators

Characterization of weakly compact disjointness preserving operators

Insights into the structure of such operators in differentiable function spaces

Abstract

A pair of functions defined on a set X with values in a vector space E is said to be disjoint if at least one of the functions takes the value 0 at every point in X. An operator acting between vector-valued function spaces is disjointness preserving if it maps disjoint functions to disjoint functions. We characterize compact and weakly compact disjointness preserving operators between spaces of Banach space-valued differentiable functions.