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.
W. Szlenk (1968)
Studia Mathematica
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Michał Kisielewicz (1989)
Annales Polonici Mathematici
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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.
Ljubomir Ćirić (1984)
Publications de l'Institut Mathématique
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M.R. Taskovic (1976)
Publications de l'Institut Mathématique [Elektronische Ressource]
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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.
William Johnson (1976)
Studia Mathematica
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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.
Maria D. Acosta, Vicente Montesinos (2006)
Acta Universitatis Carolinae. Mathematica et Physica
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Stanisław Prus
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CONTENTSIntroduction................................................................................................................................5I. Basic notations and definitions................................................................................................7II. Basic properties of finite-dimensional decompositions with (p,q)-estimates............................8III. A construction of f.d.d.'s satisfying (p,q)-estimates and its geometric applications...............13IV....
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.