941 resultados para Differential calculus in Banach spaces
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We consider the question whether there exists a Banach space X of density continuum such that every Banach space of density at most continuum isomorphically embeds into X (called a universal Banach space of density c). It is well known that a""(a)/c (0) is such a space if we assume the continuum hypothesis. Some additional set-theoretic assumption is indeed needed, as we prove in the main result of this paper that it is consistent with the usual axioms of set-theory that there is no universal Banach space of density c. Thus, the problem of the existence of a universal Banach space of density c is undecidable using the usual axioms of set-theory. We also prove that it is consistent that there are universal Banach spaces of density c, but a""(a)/c (0) is not among them. This relies on the proof of the consistency of the nonexistence of an isomorphic embedding of C([0, c]) into a""(a)/c (0).
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We analyse several examples of separable Banach spaces, some of them new, and relate them to several dichotomies obtained in [11], by classifying them according to which side of the dichotomies they fall.
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Let vv be a weight sequence on ZZ and let ψ,φψ,φ be complex-valued functions on ZZ such that φ(Z)⊂Zφ(Z)⊂Z. In this paper we study the boundedness, compactness and weak compactness of weighted composition operators Cψ,φCψ,φ on predual Banach spaces c0(Z,1/v)c0(Z,1/v) and dual Banach spaces ℓ∞(Z,1/v)ℓ∞(Z,1/v) of Beurling algebras ℓ1(Z,v)ℓ1(Z,v).
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Mode of access: Internet.
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Mode of access: Internet.
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Mode of access: Internet.
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Includes index.
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Mode of access: Internet.
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This paper was extensively circulated in manuscript form beginning in the Summer of 1989. It is being published here for the first time in its original form except for minor corrections, updated references and some concluding comments.
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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.
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The main concern of this paper is to present some improvements to results on the existence or non-existence of countably additive Borel measures that are not Radon measures on Banach spaces taken with their weak topologies, on the standard axioms (ZFC) of set-theory. However, to put the results in perspective we shall need to say something about consistency results concerning measurable cardinals.
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Mathematics Subject Classification: 26A33, 93C83, 93C85, 68T40
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Mathematics Subject Classification 2010: 26A33, 33E12, 35S10, 45K05.
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MSC 2010: 34A08 (main), 34G20, 80A25
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2010 Mathematics Subject Classification: 47B33, 47B38.