On the constant of Lipschitz approximability

Abstract

In this note we find λ > 1 \lambda >1 and give an explicit construction of a separable Banach space X X such that there is no λ \lambda -Lipschitz retraction from X X onto any compact convex subset of X X whose closed linear span is X 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.