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Displaying similar documents to “Stable points of unit ball in Orlicz spaces”

Copies of l 1 and c o in Musielak-Orlicz sequence spaces

Ghassan Alherk, Henryk Hudzik (1994)

Commentationes Mathematicae Universitatis Carolinae

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Criteria in order that a Musielak-Orlicz sequence space l Φ contains an isomorphic as well as an isomorphically isometric copy of l 1 are given. Moreover, it is proved that if Φ = ( Φ i ) , where Φ i are defined on a Banach space, X does not satisfy the δ 2 o -condition, then the Musielak-Orlicz sequence space l Φ ( X ) of X -valued sequences contains an almost isometric copy of c o . In the case of X = I R it is proved also that if l Φ contains an isomorphic copy of c o , then Φ does not satisfy the δ 2 o -condition. These results...

On some properties for dual spaces of Musielak-Orlicz function spaces

Zenon Zbąszyniak (2011)

Banach Center Publications

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We will present relationships between the modular ρ* and the norm in the dual spaces ( L Φ ) * in the case when a Musielak-Orlicz space L Φ is equipped with the Orlicz norm. Moreover, criteria for extreme points of the unit sphere of the dual space ( L ⁰ Φ ) * will be presented.

On the distribution of random variables corresponding to Musielak-Orlicz norms

David Alonso-Gutiérrez, Sören Christensen, Markus Passenbrunner, Joscha Prochno (2013)

Studia Mathematica

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Given a normalized Orlicz function M we provide an easy formula for a distribution such that, if X is a random variable distributed accordingly and X₁,...,Xₙ are independent copies of X, then 1 / C p | | x | | M ≤ | | ( x i X i ) ⁿ i = 1 | | p ≤ C p | | x | | M , where C p is a positive constant depending only on p. In case p = 2 we need the function t ↦ tM’(t) - M(t) to be 2-concave and as an application immediately obtain an embedding of the corresponding Orlicz spaces into L₁[0,1]. We also provide a general result replacing the ℓ p -norm by an arbitrary...

Geometry of Orlicz spaces

Chen Shutao

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CONTENTSPreface..............................................................................................................................4Introduction........................................................................................................................51. Orlicz spaces..................................................................................................................6 1.1. Orlicz functions...........................................................................................................6 1.2....

On the k-convexity of the Besicovitch-Orlicz space of almost periodic functions with the Orlicz norm

Fazia Bedouhene, Mohamed Morsli (2007)

Colloquium Mathematicae

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Boulahia and the present authors introduced the Orlicz norm in the class B ϕ -a.p. of Besicovitch-Orlicz almost periodic functions and gave several formulas for it; they also characterized the reflexivity of this space [Comment. Math. Univ. Carolin. 43 (2002)]. In the present paper, we consider the problem of k-convexity of B ϕ -a.p. with respect to the Orlicz norm; we give necessary and sufficient conditions in terms of strict convexity and reflexivity.

Inductive limit topologies on Orlicz spaces

Marian Nowak (1991)

Commentationes Mathematicae Universitatis Carolinae

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Let L ϕ be an Orlicz space defined by a convex Orlicz function ϕ and let E ϕ be the space of finite elements in L ϕ (= the ideal of all elements of order continuous norm). We show that the usual norm topology 𝒯 ϕ on L ϕ restricted to E ϕ can be obtained as an inductive limit topology with respect to some family of other Orlicz spaces. As an application we obtain a characterization of continuity of linear operators defined on E ϕ .