Abstract
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 enjoys the Bounded Approximation Property. This is a partial solution to a question raised by Godefroy and Ozawa.
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This research was supported by CAAS CZ.02.1.01/0.0/0.0/16-019/0000778, by the project SGS22/053/OHK3/1T/13 and by the project GA23-04776S.
Rubén Medina research has also been supported by MICINN (Spain) Project PGC2018-093794-B-I00 and MIU (Spain) FPU19/04085 Grant.
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Hájek, P., Medina, R. Retractions and the bounded approximation property in Banach spaces. Mediterr. J. Math. 20, 75 (2023). https://doi.org/10.1007/s00009-023-02270-z
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DOI: https://doi.org/10.1007/s00009-023-02270-z