This is an announcement for the paper "Some equivalence relations which are Borel reducible to isomorphism between separable Banach spaces" by Valentin Ferenczi and Eloi Medina Galego.
Abstract: 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 $L_p, 1 \leq p <2$.
Archive classification: Functional Analysis; Logic
Mathematics Subject Classification: 03E15; 46B03
Remarks: 22 pages; 2 figures
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Submitted from: eloi@ime.usp.br
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