2007•Mathematical logic quarterlyRequires access

Computing the complexity of the relation of isometry between separable Banach spaces

Julien Melleray

Abstract

Abstract We compute here the Borel complexity of the relation of isometry between separable Banach spaces, using results of Gao, Kechris [2], Mayer‐Wolf [5], and Weaver [8]. We show that this relation is Borel bireducible to the universal relation for Borel actions of Polish groups. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Key concepts: Mathematics, Separable space, Isometry (Riemannian geometry), Relation (database), Banach space, Borel equivalence relation, Pure mathematics, Discrete mathematics