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Some descriptive set-theoretic properties of the isomorphism relation between Banach spaces


Author: Andrzej Komisarski
Journal: Proc. Amer. Math. Soc. 129 (2001), 3085-3090
MSC (2000): Primary 03E15; Secondary 46B03
DOI: https://doi.org/10.1090/S0002-9939-01-05925-1
Published electronically: April 2, 2001
MathSciNet review: 1840115
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Abstract:

Consider the space $\mathcal{V} (E)$ of closed linear subspaces of a separable Banach space $E$equipped with the standard Effros Borel structure. The isomorphism relation between Banach spaces being elements of  $\mathcal{V}(E)$ determines a partition of  $\mathcal{V}(E)$. In this note we prove a result describing the complexity of analytic subsets of  $\mathcal{V}(E)$ intersecting a large enough number of the above-mentioned parts of  $\mathcal{V}(E)$.


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Additional Information

Andrzej Komisarski
Affiliation: Department of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland
Email: andkom@mimuw.edu.pl

DOI: https://doi.org/10.1090/S0002-9939-01-05925-1
Received by editor(s): July 28, 1999
Received by editor(s) in revised form: March 5, 2000
Published electronically: April 2, 2001
Communicated by: Alan Dow
Article copyright: © Copyright 2001 American Mathematical Society

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