Displaying similar documents to “A coding of separable Banach spaces. Analytic and coanalytic families of Banach spaces”

Non-universal families of separable Banach spaces

Ondřej Kurka (2016)

Studia Mathematica

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We prove that if 𝓒 is a family of separable Banach spaces which is analytic with respect to the Effros Borel structure and no X ∈ 𝓒 is isometrically universal for all separable Banach spaces, then there exists a separable Banach space with a monotone Schauder basis which is isometrically universal for 𝓒 but not for all separable Banach spaces. We also establish an analogous result for the class of strictly convex spaces.

On unconditionally saturated Banach spaces

Pandelis Dodos, Jordi Lopez-Abad (2008)

Studia Mathematica

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We prove a structural property of the class of unconditionally saturated separable Banach spaces. We show, in particular, that for every analytic set 𝓐, in the Effros-Borel space of subspaces of C[0,1], of unconditionally saturated separable Banach spaces, there exists an unconditionally saturated Banach space Y, with a Schauder basis, that contains isomorphic copies of every space X in the class 𝓐.

On the complexity of some classes of Banach spaces and non-universality

Bruno M. Braga (2014)

Czechoslovak Mathematical Journal

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These notes are dedicated to the study of the complexity of several classes of separable Banach spaces. We compute the complexity of the Banach-Saks property, the alternating Banach-Saks property, the complete continuous property, and the LUST property. We also show that the weak Banach-Saks property, the Schur property, the Dunford-Pettis property, the analytic Radon-Nikodym property, the set of Banach spaces whose set of unconditionally converging operators is complemented in its bounded...

Some strongly bounded classes of Banach spaces

Pandelis Dodos, Valentin Ferenczi (2007)

Fundamenta Mathematicae

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We show that the classes of separable reflexive Banach spaces and of spaces with separable dual are strongly bounded. This gives a new proof of a recent result of E. Odell and Th. Schlumprecht, asserting that there exists a separable reflexive Banach space containing isomorphic copies of every separable uniformly convex Banach space.

Quotients of Banach spaces and surjectively universal spaces

Pandelis Dodos (2010)

Studia Mathematica

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We characterize those classes 𝓒 of separable Banach spaces for which there exists a separable Banach space Y not containing ℓ₁ and such that every space in the class 𝓒 is a quotient of Y.

Representable Banach Spaces and Uniformly Gateaux-Smooth Norms

Frontisi, Julien (1996)

Serdica Mathematical Journal

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It is proved that a representable non-separable Banach space does not admit uniformly Gâteaux-smooth norms. This is true in particular for C(K) spaces where K is a separable non-metrizable Rosenthal compact space.

The Point of Continuity Property: Descriptive Complexity and Ordinal Index

Bossard, Benoit, López, Ginés (1998)

Serdica Mathematical Journal

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∗ Supported by D.G.I.C.Y.T. Project No. PB93-1142 Let X be a separable Banach space without the Point of Continuity Property. When the set of closed subsets of its closed unit ball is equipped with the standard Effros-Borel structure, the set of those which have the Point of Continuity Property is non-Borel. We also prove that, for any separable Banach space X, the oscillation rank of the identity on X (an ordinal index which quantifies the Point of Continuity Property) is determined...

Some results in representable Banach spaces.

Miguel Angel Canela (1988)

Publicacions Matemàtiques

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Some results are presented, concerning a class of Banach spaces introduced by G. Godefroy and M. Talagrand, the representable Banach spaces. The main aspects considered here are the stability in forming tensor products, and the topological properties of the weak* dual unitball.

On a decomposition of Banach spaces

Jakub Duda (2007)

Colloquium Mathematicae

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By using D. Preiss' approach to a construction from a paper by J. Matoušek and E. Matoušková, and some results of E. Matoušková, we prove that we can decompose a separable Banach space with modulus of convexity of power type p as a union of a ball small set (in a rather strong symmetric sense) and a set which is Aronszajn null. This improves an earlier unpublished result of E. Matoušková. As a corollary, in each separable Banach space with modulus of convexity of power type p, there...

Kadec norms and Borel sets in a Banach space

M. Raja (1999)

Studia Mathematica

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We introduce a property for a couple of topologies that allows us to give simple proofs of some classic results about Borel sets in Banach spaces by Edgar, Schachermayer and Talagrand as well as some new results. We characterize the existence of Kadec type renormings in the spirit of the new results for LUR spaces by Moltó, Orihuela and Troyanski.