On separable Banach spaces containing all separable reflexive Banach spaces
Przemysław Wojtaszczyk (1971)
Studia Mathematica
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Displaying similar documents to “The non-existence of a separable reflexive Banach space universal for all separable reflexive Banach spaces”
On separable Banach spaces containing all separable reflexive Banach spaces
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.
Classes of nonseparable Banach spaces with no universal element
V. Farmaki (1986)
Studia Mathematica
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On norm-attaining functionals
Maria D. Acosta, Vicente Montesinos (2006)
Acta Universitatis Carolinae. Mathematica et Physica
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The controlled separable projection property for Banach spaces
Jesús Ferrer, Marek Wójtowicz (2011)
Open Mathematics
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Let X, Y be two Banach spaces. We say that Y is a quasi-quotient of X if there is a continuous operator R: X → Y such that its range, R(X), is dense in Y. Let X be a nonseparable Banach space, and let U, W be closed subspaces of X and Y, respectively. We prove that if X has the Controlled Separable Projection Property (CSPP) (this is a weaker notion than the WCG property) and Y is a quasi-quotient of X, then the structure of Y resembles the structure of a separable Banach space: (a)...
On Kadec-Klee norms on Banach spaces
Dick van Dulst, Ivan Singer (1976)
Studia Mathematica
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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.
Complemented and uncomplemented subspaces of Banach spaces.
Anatolij M. Plichko, David Yost (2000)
Extracta Mathematicae
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Does a given Banach space have any non-trivial complemented subspaces? Usually, the answer is: yes, quite a lot. Sometimes the answer is: no, none at all.
Existence, uniqueness and continuous dependence of solutions of differential equations in Banach space
Michał Kisielewicz (1989)
Annales Polonici Mathematici
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On complementably universal Banach spaces
M. Kadec (1971)
Studia Mathematica
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The topological complexity of sets of convex differentiable functions.
Mohammed Yahdi (1998)
Revista Matemática Complutense
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Let C(X) be the set of all convex and continuous functions on a separable infinite dimensional Banach space X, equipped with the topology of uniform convergence on bounded subsets of X. We show that the subset of all convex Fréchet-differentiable functions on X, and the subset of all (not necessarily equivalent) Fréchet-differentiable norms on X, reduce every coanalytic set, in particular they are not Borel-sets.
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.