On the constant of Lipschitz approximability

arXiv2304.12042MaRDI QIDQ6434095

Rubén Medina

Publication date: 24 April 2023

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 represent the first known example with such a property.

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Retraction (54C15) Nonlinear classification of Banach spaces; nonlinear quotients (46B80) Lipschitz and coarse geometry of metric spaces (51F30)

This page was built for publication: On the constant of Lipschitz approximability