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Displaying similar documents to “Equality of the Lebesgue and the inductive dimension functions for compact spaces with a uniform convexity”

Uniform G-Convexity for Vector-Valued Lp Spaces

Boyko, Nataliia, Kadets, Vladimir (2009)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 46B20. Uniform G-convexity of Banach spaces is a recently introduced natural generalization of uniform convexity and of complex uniform convexity. We study conditions under which uniform G-convexity of X passes to the space of X-valued functions Lp (m,X).

Generalized midconvexity

Jacek Tabor, Józef Tabor, Krzysztof Misztal (2013)

Banach Center Publications

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There are many types of midconvexities, for example Jensen convexity, t-convexity, (s,t)-convexity. We provide a uniform framework for all the above mentioned midconvexities by considering a generalized middle-point map on an abstract space X. We show that we can define and study the basic convexity properties in this setting.

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.

Variations of uniform completeness related to realcompactness

Miroslav Hušek (2017)

Commentationes Mathematicae Universitatis Carolinae

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Various characterizations of realcompactness are transferred to uniform spaces giving non-equivalent concepts. Their properties, relations and characterizations are described in this paper. A Shirota-like characterization of certain uniform realcompactness proved by Garrido and Meroño for metrizable spaces is generalized to uniform spaces. The paper may be considered as a unifying survey of known results with some new results added.