20 resultados para Banach Lattice

em Bulgarian Digital Mathematics Library at IMI-BAS


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2000 Mathematics Subject Classification: 46B28, 47D15.

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Research partially supported by a grant of Caja de Ahorros del Mediterraneo.

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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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We prove that if a Banach space X admits a Lipschitz β-smooth bump function, then (X ∗ , weak ∗ ) is fragmented by a metric, generating a topology, which is stronger than the τβ -topology. We also use this to prove that if X ∗ admits a Lipschitz Gateaux-smooth bump function, then X is sigma-fragmentable.

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* This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95.

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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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* This work was supported by the CNR while the author was visiting the University of Milan.

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We prove that if f is a real valued lower semicontinuous function on a Banach space X and if there exists a C^1, real valued Lipschitz continuous function on X with bounded support and which is not identically equal to zero, then f is Lipschitz continuous of constant K provided all lower subgradients of f are bounded by K. As an application, we give a regularity result of viscosity supersolutions (or subsolutions) of Hamilton-Jacobi equations in infinite dimensions which satisfy a coercive condition. This last result slightly improves some earlier work by G. Barles and H. Ishii.

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A new, unified presentation of the ideal norms of factorization of operators through Banach lattices and related ideal norms is given.

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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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A dichotomysimilar property for a class of homogeneous differential equations in an arbitrary Banach space is introduced. By help of them, existence of quasi bounded solutions of the appropriate nonhomogeneous equation is proved.

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2000 Mathematics Subject Classification: 46B26, 46B03, 46B04.

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2000 Mathematics Subject Classification: Primary 40C99, 46B99.

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AMS Subject Classification 2010: 41A25, 41A35, 41A40, 41A63, 41A65, 42A38, 42A85, 42B10, 42B20