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

Komisarski, Andrzej

doi:10.1090/S0002-9939-01-05925-1

Some descriptive set-theoretic properties of the isomorphism relation between Banach spaces
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Proc. Amer. Math. Soc. 129 (2001), 3085-3090 Request permission

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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