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

• Autorzy: Benoit Bossard
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 172
• Numer: 2
• Strony: 117-152

Daty

wydano

2002

Twórcy

autor

Benoit Bossard

• Université Paris 6, Équipe d'Analyse, Boîte 186, 4 place Jussieu, 75252 Paris Cedex 05, France

Identyfikatory

DOI

10.4064/fm172-2-3