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A coding of separable Banach spaces. Analytic and coanalytic families of Banach spaces

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Bossard B.

Fundamenta Mathematicae

2002

tom 172

nr 2

117-152

When the set of closed subspaces of C(Δ), where Δ is the Cantor set, is equipped with the standard Effros-Borel structure, the graph of the basic relations between Banach spaces (isomorphism, being isomorphic to a subspace, quotient, direct sum,...) is analytic non-Borel. Many natural families of Banach spaces (such as reflexive spaces, spaces not containing ℓ₁(ω),...) are coanalytic non-Borel. Some natural ranks (rank of embedding, Szlenk indices) are shown to be coanalytic ranks. Applications are given to universality questions. Analogous results are shown for basic sequences modulo equivalence.

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1 Fundamenta Mathematicae

1 Bossard B.

1 2002

Wyniki wyszukiwania

A coding of separable Banach spaces. Analytic and coanalytic families of Banach spaces