Displaying similar documents to “Weak star and bounded weak star continuity of Banach algebra products”

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

Marián Fabian (1991)

Studia Mathematica

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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.

Weak-star continuous homomorphisms and a decomposition of orthogonal measures

B. J. Cole, Theodore W. Gamelin (1985)

Annales de l'institut Fourier

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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 ⊥ ∩ 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.

The weak Phillips property

Ali Ülger (2001)

Colloquium Mathematicae

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Let X be a Banach space. If the natural projection p:X*** → X* is sequentially weak*-weak continuous then the space X is said to have the weak Phillips property. We present several characterizations of the spaces having this property and study its relationships to other Banach space properties, especially the Grothendieck property.

On sequential properties of Banach spaces, spaces of measures and densities

Piotr Borodulin-Nadzieja, Grzegorz Plebanek (2010)

Czechoslovak Mathematical Journal

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We show that a conjunction of Mazur and Gelfand-Phillips properties of a Banach space E can be naturally expressed in terms of * continuity of seminorms on the unit ball of E * . We attempt to carry out a construction of a Banach space of the form C ( K ) which has the Mazur property but does not have the Gelfand-Phillips property. For this purpose we analyze the compact spaces on which all regular measures lie in the * sequential closure of atomic measures, and the set-theoretic properties of...