Funciones unimodulares y acotación uniforme.

J. Fernández; S. Hui; Harold S. Shapiro

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Michael Cwikel (1975)

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For $1 < p < \infty$ , a characterization is given of the dual space of weak $L^{p}$ taken over a non atomic measure space.

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In this article, we consider the (weak) drop property, weak property (a), and property (w) for closed convex sets. Here we give some relations between those properties. Particularly, we prove that C has (weak) property (a) if and only if the subdifferential mapping of Cº is (n-n) (respectively, (n-w)) upper semicontinuous and (weak) compact valued. This gives an extension of a theorem of Giles and the first author.

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We consider the set $S (μ)$ of complex-valued homomorphisms of a uniform algebra $A$ which are weak-star continuous with respect to a fixed measure $μ$ . The $μ$ -parts of $S (μ)$ are defined, and a decomposition theorem for measures in $A^{⊥} \cap L^{1} (μ)$ is obtained, in which constituent summands are mutually absolutely continuous with respect to representing measures. The set $S (μ)$ is studied for $T$ -invariant algebras on compact subsets of the complex plane and also for the infinite polydisc algebra.

On a dual locally uniformly rotund norm on a dual Vašák space

Marián Fabian (1991)

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We transfer a renorming method of transfer, due to G. Godefroy, from weakly compactly generated Banach spaces to Vašák, i.e., weakly K-countably determined Banach spaces. Thus we obtain a new construction of a locally uniformly rotund norm on a Vašák space. A further cultivation of this method yields the new result that every dual Vašák space admits a dual locally uniformly rotund norm.

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Donald Sarason (1968)

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In this note we exhibit points of weak*-norm continuity in the dual unit ball of the injective tensor product of two Banach spaces when one of them is a G-space.