On the structure of spaces of vector-valued Lipschitz functions

TL;DR

This paper explores the deep relationships between vector-valued Lipschitz function spaces and operator spaces, using these links to analyze duality, Schur properties, and norm attainment in these spaces and their preduals.

Contribution

It introduces new insights into the structure of vector-valued Lipschitz spaces and their connections to operator spaces, advancing understanding of their duality and norm properties.

Findings

Established strong links between Lipschitz function spaces and operator spaces.

Analyzed duality and Schur properties in these spaces.

Studied norm attainment and predual structures.

Abstract

We analyse the strong connections between spaces of vector-valued Lipschitz functions and spaces of linear continuous operators. We apply these links to study duality, Schur properties and norm attainment in the former class of spaces as well as in their canonical preduals