Displaying similar documents to “Strongly exposed points in Musielak-Orlicz sequence spaces endowed with Orlicz norm”

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 ) 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 p -norm by an arbitrary...

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 Φ ) * will be presented.

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.

An operator characterization of L p -spaces in a class of Orlicz spaces

Maciej Burnecki (2008)

Banach Center Publications

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We consider an embedding of the group of invertible transformations of [0,1] into the algebra of bounded linear operators on an Orlicz space. We show that if this embedding preserves the group action then the Orlicz space is an L p -space for some 1 ≤ p < ∞.

Geometry of Orlicz spaces

Chen Shutao

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

Fenchel-Orlicz spaces

Barry Turett

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CONTENTSIntroduction............................................................................... 51. Definitions and preliminary results......................................... 72. Completeness of L Φ ( μ , ) .............................. 93. Linear functionals on L Φ ( μ , ) ....................... 264. Geometry of Fenchel-Orlicz spaces........................................ 41References....................................................................................... 54

Cantor-Bernstein theorems for Orlicz sequence spaces

Carlos E. Finol, Marcos J. González, Marek Wójtowicz (2014)

Banach Center Publications

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For two Banach spaces X and Y, we write d i m ( X ) = d i m ( Y ) if X embeds into Y and vice versa; then we say that X and Y have the same linear dimension. In this paper, we consider classes of Banach spaces with symmetric bases. We say that such a class ℱ has the Cantor-Bernstein property if for every X,Y ∈ ℱ the condition d i m ( X ) = d i m ( Y ) implies the respective bases (of X and Y) are equivalent, and hence the spaces X and Y are isomorphic. We prove (Theorems 3.1, 3.3, 3.5) that the class of Orlicz sequence spaces generated...

Reflexive subspaces of some Orlicz spaces

Emmanuelle Lavergne (2008)

Colloquium Mathematicae

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We show that when the conjugate of an Orlicz function ϕ satisfies the growth condition Δ⁰, then the reflexive subspaces of L ϕ are closed in the L¹-norm. For that purpose, we use (and give a new proof of) a result of J. Alexopoulos saying that weakly compact subsets of such L ϕ have equi-absolutely continuous norm.

A Simpler Proof of the Negative Association Property for Absolute Values of Measures Tied to Generalized Orlicz Balls

Jakub Onufry Wojtaszczyk (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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Negative association for a family of random variables ( X i ) means that for any coordinatewise increasing functions f,g we have ( X i , . . . , X i k ) g ( X j , . . . , X j l ) f ( X i , . . . , X i k ) g ( X j , . . . , X j l ) for any disjoint sets of indices (iₘ), (jₙ). It is a way to indicate the negative correlation in a family of random variables. It was first introduced in 1980s in statistics by Alem Saxena and Joag-Dev Proschan, and brought to convex geometry in 2005 by Wojtaszczyk Pilipczuk to prove the Central Limit Theorem for Orlicz balls. The paper gives a relatively simple...

Calderón couples of rearrangement invariant spaces

N. Kalton (1993)

Studia Mathematica

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We examine conditions under which a pair of rearrangement invariant function spaces on [0,1] or [0,∞) form a Calderón couple. A very general criterion is developed to determine whether such a pair is a Calderón couple, with numerous applications. We give, for example, a complete classification of those spaces X which form a Calderón couple with L . We specialize our results to Orlicz spaces and are able to give necessary and sufficient conditions on an Orlicz function F so that the pair...

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 .

Some results on packing in Orlicz sequence spaces

Y. Q. Yan (2001)

Studia Mathematica

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We present monotonicity theorems for index functions of N-fuctions, and obtain formulas for exact values of packing constants. In particular, we show that the Orlicz sequence space l ( N ) generated by the N-function N(v) = (1+|v|)ln(1+|v|) - |v| with Luxemburg norm has the Kottman constant K ( l ( N ) ) = N - 1 ( 1 ) / N - 1 ( 1 / 2 ) , which answers M. M. Rao and Z. D. Ren’s [8] problem.

Isometric classification of norms in rearrangement-invariant function spaces

Beata Randrianantoanina (1997)

Commentationes Mathematicae Universitatis Carolinae

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Suppose that a real nonatomic function space on [ 0 , 1 ] is equipped with two rearrangement-invariant norms · and | | | · | | | . We study the question whether or not the fact that ( X , · ) is isometric to ( X , | | | · | | | ) implies that f = | | | f | | | for all f in X . We show that in strictly monotone Orlicz and Lorentz spaces this is equivalent to asking whether or not the norms are defined by equal Orlicz functions, respĿorentz weights. We show that the above implication holds true in most rearrangement-invariant spaces, but we also identify...