BOREL REDUCIBILITY AND HOLDER(alpha) EMBEDDABILITY BETWEEN BANACH SPACES

作者：Ding Longyun^*

来源：Journal of Symbolic Logic, 2012, 77(1): 224-244.

We investigate Borel reducibility between equivalence relations E(X; p) X-N/l(P),(X)'s where X is a separable Banach space. We show that this reducibility is related to the so called Holder(alpha) 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(L-r; p)'s and E(c(0); p)'s for r, p is an element of [1, + infinity).
We also answer a problem presented by Kanovei in the affirmative by showing that C(R+)/C-0(R+) is Borel bireducible to R-N/c(0).

• 出版日期2012-3
• 单位南开大学