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.
Henryk Hudzik, Paweł Kolwicz (2004)
Studia Mathematica
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We study property (β) in Köthe-Bochner sequence spaces E(X), where E is any Köthe sequence space and X is an arbitrary Banach space. The question of whether or not this geometric property lifts from X and E to E(X) is examined. We prove that if dim X = ∞, then E(X) has property (β) if and only if X has property (β) and E is orthogonally uniformly convex. It is also showed that if dim X < ∞, then E(X) has property (β) if and only if E has property (β). Our results essentially extend...
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).
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.
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.
Jan van Mill, Marcel van de Vel (1986)
Colloquium Mathematicae
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A. Kamińska (1984)
Studia Mathematica
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Elisabetta Maluta, Pier Luigi Papini (2009)
Colloquium Mathematicae
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In reflexive Banach spaces with some degree of uniform convexity, we obtain estimates for Kottman's separation constant in terms of the corresponding modulus.
S. Chen, Henryk Hudzik (1988)
Commentationes Mathematicae Universitatis Carolinae
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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.
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.
Yunan Cui, Henryk Hudzik, Ryszard Płuciennik (1997)
Annales Polonici Mathematici
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E.H. Lieb, Keith Ball, E.A. Carlen (1994)
Inventiones mathematicae
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Eva A. Gallardo-Gutiérrez, Jonathan R. Partington (2005)
Studia Mathematica
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We show that the Angle Criterion for testing supercyclic vectors depends in an essential way on the geometrical properties of the underlying space. In particular, we exhibit non-supercyclic vectors for the backward shift acting on c₀ that still satisfy such a criterion. Nevertheless, if ℬ is a locally uniformly convex Banach space, the Angle Criterion yields an equivalent condition for a vector to be supercyclic. Furthermore, we prove that local uniform convexity cannot be weakened to...