Borel reducibility and Holder($α$) embeddability between Banach spaces

Details Borel reducibility and Holder($α$) embeddability between Banach spaces Borel reducibility and Holder($α$) embeddability between Banach spaces

2009-12-10

arxiv.org/abs/0912.1912v1

Mathematics

Logic

29 pages

Scientific paper

We investigate Borel reducibility between equivalence relations $E(X,p)=X^{\Bbb N}/\ell_p(X)$'s where $X$ is a separable Banach space. We show that this reducibility is related to the so called H\"older$(\alpha)$ 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 $r,p\in[1,+\infty)$. We also answer a problem presented by Kanovei in the affirmative by showing that $C({\Bbb R}^+)/C_0({\Bbb R}^+)$ is Borel bireducible to ${\Bbb R}^{\Bbb N}/c_0$.

Affiliated with

Also associated with

No associations

Rating

Borel reducibility and Holder($α$) embeddability between Banach spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Borel reducibility and Holder($α$) embeddability between Banach spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Borel reducibility and Holder($α$) embeddability between Banach spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-594288