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Note on almost isometric ideals and local retracts in Banach and metric spaces
Part of
- Model theory
- Normed linear spaces and Banach spaces; Banach lattices
Leandro Candido, Marek Cúth, Ondřej Smetana
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View

Published online by Cambridge University Press:

27 August 2024, pp. 1-25
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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.

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Note on almost isometric ideals and local retracts in Banach and metric spaces