# 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} }

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

- MathematicsJournal of Mathematical Analysis and Applications
- 2022

Retractions and the bounded approximation property in Banach spaces

- Mathematics
- 2022

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…

Schauder basis in Lipschitz free spaces over nets of $\mathcal{L}_\infty$-spaces

- Mathematics
- 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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