Displaying similar documents to “On the non-existence of linear isomorphisms between Banach spaces of analytic functions of one and several complex variables”

Generalized Analytic and Quasi-Analytic Vectors

Jan Rusinek (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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For every sequence (aₙ) of positive real numbers and an operator acting in a Banach space, we introduce the families of (aₙ)-analytic and (aₙ)-quasi-analytic vectors. We prove various properties of these families.

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

Benoit Bossard (2002)

Fundamenta Mathematicae

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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...