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arXiv · 1704.06961

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

Olesia Zavarzina
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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.

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Olesia Zavarzina. 2018-07-13. Non-expansive bijections between unit balls of Banach spaces (A technical version with some boring proofs included). https://doi.org/10.1215/20088752-2017-0050

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