Extension of isometries between unit spheres of finite-dimensional polyhedral Banach spaces

TL;DR

This paper proves that any onto isometry between the unit spheres of finite-dimensional polyhedral Banach spaces can be extended to a linear isometry of the entire spaces, highlighting a structural rigidity property.

Contribution

It establishes a new extension result for isometries in finite-dimensional polyhedral Banach spaces, generalizing previous known cases.

Findings

Onto isometries extend to linear isometries

Extension applies specifically to finite-dimensional polyhedral Banach spaces

Results contribute to understanding geometric structure of Banach spaces

Abstract

We prove that an onto isometry between unit spheres of finite-dimensional polyhedral Banach spaces extends to a linear isometry of the corresponding spaces.