The Kottman constant for $\alpha$-H\"older maps

TL;DR

This paper explores how the Kottman constant of a Banach space influences the extension properties of $eta$-H"older maps for all $eta$ in (0,1], providing insights into geometric functional analysis.

Contribution

It introduces a novel connection between the Kottman constant and the extendability of $eta$-H"older maps in Banach spaces.

Findings

The Kottman constant affects the extendability of $eta$-H"older maps.

Characterization of Banach spaces based on the Kottman constant.

New criteria for extension of H"older maps derived from geometric properties.

Abstract

We investigate the role of the Kottman constant of a Banach space $X$ in the extension of $\alpha$-H\"older continuous maps for every $\alpha\in (0,1]$.