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Borel reductibility and Hölder (α) embeddability between Banach spaces

Published online by Cambridge University Press:  12 March 2014

Longyun Ding
Longyun Ding*
Affiliation:
School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, P.R.China, E-mail: dingly@nankai.edu.cn
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Abstract

We investigate Borel reducibility between equivalence relations E(X; p) = Xℕ/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 Є [1, +∞).

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

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 1 , March 2012 , pp. 224 - 244
Copyright
Copyright © Association for Symbolic Logic 2012

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