Every 2-dimensional Banach space has the Mazur-Ulam property

Abstract

We prove that every isometry between the unit spheres of 2-dimensional Banach spaces extends to a linear isometry of the Banach spaces. This resolves the famous Tingley's problem in the class of 2-dimensional Banach spaces.

8 pages

References in corpus (1)

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

Cited by in corpus (1)

• On the concept of non-ultrametric non-Archimedean analysis