Displaying similar documents to “Cesàro wedge and weak Cesàro wedge F K -spaces”

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.

Weak Cauchy sequences in L ∞ ( μ , X )

Georg Schlüchtermann (1995)

Studia Mathematica

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For a finite and positive measure space Ω,∑,μ characterizations of weak Cauchy sequences in L ∞ ( μ , X ) , the space of μ-essentially bounded vector-valued functions f:Ω → X, are presented. The fine distinction between Asplund and conditionally weakly compact subsets of L ∞ ( μ , X ) is discussed.

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.