Free objects in Banach space theory
Enrique Garc\'ia-S\'anchez, David de Hevia, Pedro Tradacete
TL;DR
This paper surveys recent advances in the theory of free objects in Banach space theory, focusing on Lipschitz free spaces, holomorphic free spaces, and free Banach lattices, highlighting their interrelations.
Contribution
It provides a comprehensive overview of recent progress and parallels among different types of free objects in Banach space theory.
Findings
Identifies common themes among Lipschitz free spaces, holomorphic free spaces, and free Banach lattices.
Highlights recent breakthroughs in understanding the structure of these free objects.
Draws connections between different free object constructions in Banach space theory.
Abstract
We survey recent progress on three relevant instances of free objects related to Banach spaces: Lipschitz free spaces generated by metric spaces, holomorphic free spaces generated by open sets and free Banach lattices generated by Banach spaces. Our emphasis will be on the parallelisms among these developments.
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Taxonomy
TopicsAdvanced Banach Space Theory · Advanced Topology and Set Theory