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March 2012 Borel reducibility and Hölder(α) embeddability between Banach spaces
Longyun Ding
J. Symbolic Logic 77(1): 224-244 (March 2012). DOI: 10.2178/jsl/1327068700

Abstract

We investigate Borel reducibility between equivalence relations E(X;p)=X/ℓp(X)'s where X is a separable Banach space. We show that this reducibility is related to the so called Hölder(α) embeddability between Banach spaces. By using the notions of type and cotype of Banach spaces, we present many results on reducibility and unreducibility between E(Lr;p)'s and E(c₀;p)'s for r,p∈[1,+∞).

We also answer a problem presented by Kanovei in the affirmative by showing that C(ℝ⁺)/C₀(ℝ⁺) is Borel bireducible to ℝ/c₀.

Citation

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Longyun Ding. "Borel reducibility and Hölder(α) embeddability between Banach spaces." J. Symbolic Logic 77 (1) 224 - 244, March 2012. https://doi.org/10.2178/jsl/1327068700

Information

Published: March 2012
First available in Project Euclid: 20 January 2012

zbMATH: 1250.03082
MathSciNet: MR2951638
Digital Object Identifier: 10.2178/jsl/1327068700

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Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 1 • March 2012
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