On property (β) of Rolewicz in Köthe-Bochner sequence spaces

Henryk Hudzik; Paweł Kolwicz

Displaying similar documents to “On property (β) of Rolewicz in Köthe-Bochner sequence spaces”

Coefficient of orthogonal convexity of some Banach function spaces

Paweł Kolwicz, Stefan Rolewicz (2004)

Studia Mathematica

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We study orthogonal uniform convexity, a geometric property connected with property (β) of Rolewicz, P-convexity of Kottman, and the fixed point property (see [19, [20]). We consider the coefficient of orthogonal convexity in Köthe spaces and Köthe-Bochner spaces.

On Property β of Rolewicz in Köthe-Bochner Function Spaces

Paweł Kolwicz (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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It is proved that the Köthe-Bochner function space E(X) has property β if and only if X is uniformly convex and E has property β. In particular, property β does not lift from X to E(X) in contrast to the case of Köthe-Bochner sequence spaces.

Banach-Saks property in some Banach sequence spaces

Yunan Cui, Henryk Hudzik, Ryszard Płuciennik (1997)

Annales Polonici Mathematici

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It is proved that for any Banach space X property (β) defined by Rolewicz in [22] implies that both X and X* have the Banach-Saks property. Moreover, in Musielak-Orlicz sequence spaces, criteria for the Banach-Saks property, the near uniform convexity, the uniform Kadec-Klee property and property (H) are given.

The criteria for local uniform rotundity of Orlicz spaces

A. Kamińska (1984)

Studia Mathematica

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On some convexities of Orlicz and Orlicz-Bochner spaces

S. Chen, Henryk Hudzik (1988)

Commentationes Mathematicae Universitatis Carolinae

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Uniform non-squareness and property $(β)$ of Besicovitch-Orlicz spaces of almost periodic functions with Orlicz norm

Fatiha Boulahia, Mohamed Morsli (2010)

Commentationes Mathematicae Universitatis Carolinae

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We characterize the uniform non-squareness and the property $(β)$ of Besicovitch-Orlicz spaces of almost periodic functions equipped with Orlicz norm.

Equality of the Lebesgue and the inductive dimension functions for compact spaces with a uniform convexity

Jan van Mill, Marcel van de Vel (1986)

Colloquium Mathematicae

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On $P$ -convex Musielak-Orlicz spaces

Paweł Kolwicz, Ryszard Płuciennik (1995)

Commentationes Mathematicae Universitatis Carolinae

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In this paper there is proved that every Musielak-Orlicz space is reflexive iff it is $P$ -convex. This is an essential extension of the results given by Ye Yining, He Miaohong and Ryszard Płuciennik [16].

On the uniform convexity of the Besicovitch-Orlicz space of almost periodic functions with Orlicz norm

Mohamed Morsli, Fazia Bedouhene (2005)

Colloquium Mathematicae

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In [5], we characterized the uniform convexity with respect to the Luxemburg norm of the Besicovitch-Orlicz space of almost periodic functions. Here we give an analogous result when this space is endowed with the Orlicz norm.