Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 77, Issue 1 (2012), 224-244.
Borel reducibility and Hölder(α) embeddability between Banach spaces
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∈[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.
J. Symbolic Logic, Volume 77, Issue 1 (2012), 224-244.
First available in Project Euclid: 20 January 2012
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: Primary 03E15, 46B20, 47H99
Ding, Longyun. Borel reducibility and Hölder(α) embeddability between Banach spaces. J. Symbolic Logic 77 (2012), no. 1, 224--244. doi:10.2178/jsl/1327068700. https://projecteuclid.org/euclid.jsl/1327068700