Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): Andrzej Komisarski
Journal: Proc. Amer. Math. Soc. 129 (2001), 3085-3090.
MSC (2000): Primary 03E15; Secondary 46B03
Posted: 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 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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