Non-expansive bijections between unit balls of Banach spaces (A technical version with some boring proofs included)

Abstract

It is known that if $M$ is a finite-dimensional Banach space, or a strictly convex space, or the space ${\ell }_1$, then every non-expansive bijection $F:B_M\to B_M$ is an isometry. We extend these results to non-expansive bijections $F:B_E\to B_M$ between unit balls of two different Banach spaces. Namely, if $E$ is an arbitrary Banach space and $M$ is finite-dimensional or strictly convex, or the space ${\ell }_1$ then every non-expansive bijection $F:B_E\to B_M$ is an isometry.

References in corpus (1)

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

Cited by in corpus (1)

• Non-expansive bijections, uniformities and polyhedral faces