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May 2018 Nonexpansive bijections between unit balls of Banach spaces
Olesia Zavarzina
Ann. Funct. Anal. 9(2): 271-281 (May 2018). DOI: 10.1215/20088752-2017-0050

Abstract

It is known that if M is a finite-dimensional Banach space, or a strictly convex space, or the space 1, then every nonexpansive bijection F:BMBM of its unit ball BM is an isometry. We extend these results to nonexpansive bijections F:BEBM 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 1, then every nonexpansive bijection F:BEBM is an isometry.

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Olesia Zavarzina. "Nonexpansive bijections between unit balls of Banach spaces." Ann. Funct. Anal. 9 (2) 271 - 281, May 2018. https://doi.org/10.1215/20088752-2017-0050

Information

Received: 22 February 2017; Accepted: 11 June 2017; Published: May 2018
First available in Project Euclid: 13 January 2018

zbMATH: 06873703
MathSciNet: MR3795091
Digital Object Identifier: 10.1215/20088752-2017-0050

Subjects:
Primary: 46B20

Keywords: nonexpansive map , plastic space , strictly convex space , unit ball

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.9 • No. 2 • May 2018
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