Note on almost isometric ideals and local retracts in Banach and metric spaces
Functional Analysis
2026-03-18 v1
Abstract
We exhibit a new approach to the proofs of the existence of a large family of almost isometric ideals in nonseparable Banach spaces and existence of a large family of almost isometric local retracts in metric spaces. Our approach also implies the existence of a large family of nontrivial projections on every dual of a nonseparable Banach space. We prove three possible formulations of our results are equivalent. Some applications are mentioned which witness the usefulness of our novel approach.
Keywords
Cite
@article{arxiv.2312.07749,
title = {Note on almost isometric ideals and local retracts in Banach and metric spaces},
author = {Leandro Candido and Marek Cúth and Ondřej Smetana},
journal= {arXiv preprint arXiv:2312.07749},
year = {2026}
}
Comments
22 pages