Some equivalence relations which are Borel reducible to isomorphism between separable Banach spaces

Details Some equivalence relations which are Borel reducible to isomorphism between separable Banach spaces Some equivalence relations which are Borel reducible to isomorphism between separable Banach spaces

2004-06-23

arxiv.org/abs/math/0406477v2

Mathematics

Functional Analysis

23 pages; 2 figures

Scientific paper

We improve the known results about the complexity of the relation of isomorphism between separable Banach spaces up to Borel reducibility, and we achieve this using the classical spaces $c_0$, $\ell_p$ and $L_p$, $1 \leq p <2$. More precisely, we show that the relation $E_{K_{\sigma}}$ is Borel reducible to isomorphism and complemented biembeddability between subspaces of $c_0$ or $\ell_p, 1 \leq p <2$. We show that the relation $E_{K_{\sigma}} \otimes =^+$ is Borel reducible to isomorphism, complemented biembeddability, and Lipschitz equivalence between subspaces of $L_p, 1 \leq p <2$.

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