Separating maps between spaces of vector-valued absolutely continuous functions

TL;DR

This paper characterizes linear bijections that preserve disjointness between spaces of vector-valued absolutely continuous functions, establishing their continuity and properties in both finite and infinite-dimensional cases.

Contribution

It provides a comprehensive description of separating linear bijections on vector-valued absolutely continuous function spaces, including finite and infinite-dimensional cases.

Findings

Separating bijections are continuous and biseparating in finite-dimensional cases.

The structure of these maps is characterized for infinite-dimensional spaces.

The results extend understanding of disjointness-preserving transformations in function spaces.

Abstract

In this paper we give a description of separating or disjointness preserving linear bijections on spaces of vector-valued absolutely continuous functions defined on compact subsets of the real line. We obtain that they are continuous and biseparating in the finite-dimensional case. The infinite-dimensional case is also studied.