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arXiv · 2312.07749

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

Leandro Candido·Marek Cúth·Ondřej Smetana
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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.

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Leandro Candido, Marek Cúth, Ondřej Smetana. 2023-12-12. Note on almost isometric ideals and local retracts in Banach and metric spaces. https://doi.org/10.1017/prm.2024.68

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