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Displaying similar documents to “Every nonreflexive Banach lattice has the packaging constant equal to 1/2.”

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).

Rademacher series from Orlicz to the present day

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.

Packing in Orlicz sequence spaces

M. Rao, Z. Ren (1997)

Studia Mathematica

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We show how one can, in a unified way, calculate the Kottman and the packing constants of the Orlicz sequence space defined by an N-function, equipped with either the gauge or Orlicz norms. The values of these constants for a class of reflexive Orlicz sequence spaces are found, using a quantitative index of N-functions and some interpolation theorems. The exposition is essentially selfcontained.

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.

Weak orthogonality and weak property ( β ) in some Banach sequence spaces

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 ( β ) in Orlicz sequence spaces in the case of the Luxemburg norm as well as the Orlicz norm are given.

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.