Displaying similar documents to “Some strongly bounded classes of Banach spaces”

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.

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.

A New Hereditarily l^2 Banach Space

Petsoulas, Giorgos (2009)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 46B20, 46B26. We construct a non-reflexive, l^2 saturated Banach space such that every non-reflexive subspace has non-separable dual.