Local complementation in Banach spaces and its preservation under free constructions
Functional Analysis
2024-07-18 v4
Abstract
In this work we consider natural generalizations of local complementation in Banach spaces, which include Lipschitz-local complementation. We show that all these notions are indeed equivalent to the classical notion of local complementation of Banach spaces. As an application, we show that local complementation is naturally preserved under certain free constructions in Functional Analysis, including Lipschitz-free spaces and free Banach lattices.
Keywords
Cite
@article{arxiv.2107.11339,
title = {Local complementation in Banach spaces and its preservation under free constructions},
author = {Antonio Avilés and Gonzalo Martínez-Cervantes and Abraham Rueda Zoca},
journal= {arXiv preprint arXiv:2107.11339},
year = {2024}
}