Borel reductibility and Hölder (α) embeddability between Banach spaces
Borel reductibility and Hölder (α) embeddability between Banach spaces
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DOI：
10.2178/jsl/1327068700
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发表时间：
2012-03
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通讯作者：
Longyun Ding
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作者：
Longyun Ding
研究了等价关系E(X; p) = X∈/ p(X) s之间的Borel可约性，其中X是可分离的Banach空间。我们证明了这种可约性与Banach空间之间的Hölder（α）可嵌入性有关。利用Banach空间的型和共型的概念，给出了r， p Є[1， +∞]下E(Lr; p)'s和E(c0; p)'s之间的可约性和不可约性的许多结果。我们还肯定地回答了Kanovei提出的一个问题，证明C(∈+)/C0（∈+）是Borel双约到∈/C0的。
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.