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Displaying similar documents to “Rademacher series from Orlicz to the present day”

Mazur-Orlicz equality

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.

On Simons' version of Hahn-Banach-Lagrange theorem

Jerzy Grzybowski, Hubert Przybycień, Ryszard Urbański (2014)

Banach Center Publications

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In this paper we generalize in Theorem 12 some version of Hahn-Banach Theorem which was obtained by Simons. We also present short proofs of Mazur and Mazur-Orlicz Theorem (Theorems 2 and 3).

Weak compactness and Orlicz 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).

On property (β) of Rolewicz in Musielak-Orlicz sequence spaces equipped with the Orlicz norm

Paweł Kolwicz (2005)

Banach Center Publications

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We prove that the Musielak-Orlicz sequence space with the Orlicz norm has property (β) iff it is reflexive. It is a generalization and essential extension of the respective results from [3] and [5]. Moreover, taking an arbitrary Musielak-Orlicz function instead of an N-function we develop new methods and techniques of proof and we consider a wider class of spaces than in [3] and [5].

Jung constants of Orlicz sequence spaces

Tao Zhang (2003)

Annales Polonici Mathematici

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Estimation of the Jung constants of Orlicz sequence spaces equipped with either the Luxemburg norm or the Orlicz norm is given. The exact values of the Jung constants of a class of reflexive Orlicz sequence spaces are found by using new quantitative indices for 𝓝-functions.

Roughness of two norms on Musielak-Orlicz function spaces

Jimin Zheng, Lihuan Sun, Yun'an Cui (2008)

Banach Center Publications

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In this paper, the criteria of strong roughness, roughness and pointwise roughness of Orlicz norm and Luxemburg norm on Musielak-Orlicz function spaces are obtained.

On the KR and WKR points of Orlicz.

Yunan Cui, Yunfeng Zhang (1997)

Collectanea Mathematica

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In this paper, we obtain criteria for KR and WKR points in Orlicz function spaces equipped with the Luxemburg norm.

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.