• Corpus ID: 244478727

# Compact retractions and Schauder decompositions in Banach spaces

@inproceedings{Hajek2021CompactRA,
title={Compact retractions and Schauder decompositions in Banach spaces},
author={Petr H'ajek and Rub'en Medina},
year={2021}
}
• Published 1 June 2021
• Mathematics
In our note we show the very close connection between the existence of a Finite Dimensional Decomposition (FDD for short) for a separable Banach space X and the existence of a Lipschitz retraction of X onto a small (in a certain precise sense) generating convex and compact subset K of X. In one direction, if X admits an FDD then we construct a Lipschitz retraction onto a small generating convex and compact set K. On the other hand, we prove that if X admits a small generating compact Lipschitz…
3 Citations
Schauder bases in Lipschitz free spaces over nets in Banach spaces
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Journal of Mathematical Analysis and Applications
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Retractions and the bounded approximation property in Banach spaces
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In the present paper we prove that a necessary condition for a Banach space X to admit a generating compact Lipschitz retract K, which satisfies an additional mild assumption on its shape, is that X
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• 2022
In the present note we give a construction (based on a retractional argument) of a Schauder basis for the Lipschitz free space F(N), over a net N in any separable infinite dimensional L∞-space X. In

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