Absolute Lipschitz extendability and linear projection constants

Abstract

We prove that the absolute extendability constant of a finite metric space may be determined by computing relative projection constants of certain Lipschitz-free spaces. As an application, we show that $\mbox{ae}(3)=4/3$ and $\mbox{ae}(4)\geq (5+4\sqrt{2})/7$. Moreover, we discuss how to compute relative projection constants by solving linear programming problems.

revised version. To appear in Studia Mathematica

References in corpus (1)

• Approximating spaces of Nagata dimension zero by weighted trees

Cited by in corpus (2)

• Canonical embedding of Lipschitz-free $p$-spaces
• Lipschitz extension theorems with explicit constants