N. J. Kalton (2004)
Banach Center Publications
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We survey some questions on Rademacher series in both Banach and quasi-Banach spaces which have been the subject of extensive research from the time of Orlicz to the present day.
Fon-Che Liu (2008)
Studia Mathematica
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A remarkable theorem of Mazur and Orlicz which generalizes the Hahn-Banach theorem is here put in a convenient form through an equality which will be referred to as the Mazur-Orlicz equality. Applications of the Mazur-Orlicz equality to lower barycenters for means, separation principles, Lax-Milgram lemma in reflexive Banach spaces, and monotone variational inequalities are provided.
Hudzik, Henryk
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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.
P. G. Dodds, E. M. Semenov, F. A. Sukochev (2004)
Studia Mathematica
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This paper studies the Banach-Saks property in rearrangement invariant spaces on the positive half-line. A principal result of the paper shows that a separable rearrangement invariant space E with the Fatou property has the Banach-Saks property if and only if E has the Banach-Saks property for disjointly supported sequences. We show further that for Orlicz and Lorentz spaces, the Banach-Saks property is equivalent to separability although the separable parts of some Marcinkiewicz spaces...
Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza (2008)
Colloquium Mathematicae
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We give new proofs that some Banach spaces have Pełczyński's property (V).
Henryk Hudzik (1993)
Collectanea Mathematica
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Henryk Hudzik (1989)
Revista Matemática de la Universidad Complutense de Madrid
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P. Lefèvre, D. Li, H. Queffélec, L. Rodríguez-Piazza (2004)
Studia Mathematica
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We produce several situations where some natural subspaces of classical Banach spaces of functions over a compact abelian group contain the space c₀.
R. Williamson (1965)
Studia Mathematica
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S. Chen, Henryk Hudzik (1988)
Commentationes Mathematicae Universitatis Carolinae
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Yunan Cui, Henryk Hudzik, Ryszard Płuciennik (1999)
Czechoslovak Mathematical Journal
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It is proved that a Köthe sequence space is weakly orthogonal if and only if it is order continuous. Criteria for weak property () in Orlicz sequence spaces in the case of the Luxemburg norm as well as the Orlicz norm are given.
Henryk Hudzik, Zenon Zbaszyniak (1997)
Collectanea Mathematica
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A formula for the distance of an arbitrary element x in Musielak-Orlicz space L^Phi from the subspace E^Phi of order continuous elements is given for both (the Luxemburg and the Orlicz) norms. A formula for the norm in the dual space of L^Phi is given for any of these two norms. Criteria for smooth points and smoothness in L^Phi and E^Phi equipped with the Orlicz norm are presented.