On the constant of Lipschitz approximability

Medina, Rubén

doi:10.1090/tran/9110

On the constant of Lipschitz approximability
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by Rubén Medina

Trans. Amer. Math. Soc. 377 (2024), 2925-2945

DOI: https://doi.org/10.1090/tran/9110

Published electronically: February 20, 2024

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Abstract:

In this note we find $\lambda >1$ and give an explicit construction of a separable Banach space $X$ such that there is no $\lambda$-Lipschitz retraction from $X$ onto any compact convex subset of $X$ whose closed linear span is $X$. This is closely related to a well-known open problem raised by Godefroy and Ozawa in 2014 and represents the first known example of a Banach space with such a property.

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