# [Banach] Abstract of a paper by Valentin Ferenczi and Eloi Medina Galego

Dale Alspach alspach at www.math.okstate.edu
Fri Jun 25 11:09:04 CDT 2004

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

The source file(s), sjm16.tex: 74499 bytes, is(are) stored in gzipped
form as 0406477.gz with size 22kb. The corresponding postcript file has
gzipped size 86kb.

Submitted from: eloi at ime.usp.br

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