On separable Banach spaces containing all separable reflexive Banach spaces
Przemysław Wojtaszczyk (1971)
Studia Mathematica
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Przemysław Wojtaszczyk (1971)
Studia Mathematica
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W. Szlenk (1968)
Studia Mathematica
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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.
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.
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.
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.
M.R. Taskovic (1976)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Ljubomir Ćirić (1984)
Publications de l'Institut Mathématique
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Gunther Dirr, Vladimir Rakočević, Harald K. Wimmer (2005)
Studia Mathematica
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Let W and L be complementary subspaces of a Banach space X and let P(W,L) denote the projection on W along L. We obtain a sufficient condition for a subspace M of X to be complementary to W and we derive estimates for the norm of P(W,L) - P(W,M).
Michał Kisielewicz (1989)
Annales Polonici Mathematici
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William Johnson (1976)
Studia Mathematica
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Maria D. Acosta, Vicente Montesinos (2006)
Acta Universitatis Carolinae. Mathematica et Physica
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E. Martín Peinador, E. Induráin, A. Plans Sanz de Bremond, A. A. Rodes Usan (1988)
Revista Matemática de la Universidad Complutense de Madrid
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The main result of this paper is the following: A separable Banach space X is reflexive if and only if the infimum of the Gelfand numbers of any bounded linear operator defined on X can be computed by means of just one sequence on nested, closed, finite codimensional subspaces with null intersection.