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September 2020 Rademacher type and Enflo type coincide
Paata Ivanisvili, Ramon van Handel, Alexander Volberg
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Ann. of Math. (2) 192(2): 665-678 (September 2020). DOI: 10.4007/annals.2020.192.2.8

Abstract

A nonlinear analogue of the Rademacher type of a Banach space was introduced in classical work of Enflo. The key feature of Enflo type is that its definition uses only the metric structure of the Banach space, while the definition of Rademacher type relies on its linear structure. We prove that Rademacher type and Enflo type coincide, settling a long-standing open problem in Banach space theory. The proof is based on a novel dimension-free analogue of Pisier's inequality on the discrete cube.

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Paata Ivanisvili. Ramon van Handel. Alexander Volberg. "Rademacher type and Enflo type coincide." Ann. of Math. (2) 192 (2) 665 - 678, September 2020. https://doi.org/10.4007/annals.2020.192.2.8

Information

Published: September 2020
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.4007/annals.2020.192.2.8

Subjects:
Primary: 46B07 , 46B09 , 60E15

Keywords: ‎Banach spaces , Enflo type , Pisier's inequality , Rademacher type

Rights: Copyright © 2020 Department of Mathematics, Princeton University

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Vol.192 • No. 2 • September 2020
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