Displaying similar documents to “Isometric classification of norms in rearrangement-invariant function spaces”

Extreme compact operators from Orlicz spaces to C ( Ω )

Shutao Chen, Marek Wisła (1993)

Commentationes Mathematicae Universitatis Carolinae

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Let E ϕ ( μ ) be the subspace of finite elements of an Orlicz space endowed with the Luxemburg norm. The main theorem says that a compact linear operator T : E ϕ ( μ ) → C ( Ω ) is extreme if and only if T * ω ∈ Ext B ( ( E ϕ ( μ ) ) * ) on a dense subset of Ω , where Ω is a compact Hausdorff topological space and 〈 T * ω , x 〉 = ( T x ) ( ω ) . This is done via the description of the extreme points of the space of continuous functions C ( Ω , L ϕ ( μ ) ) , L ϕ ( μ ) being an Orlicz space equipped with the Orlicz norm (conjugate to the Luxemburg one). There is also given a theorem on closedness of the...

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 < ∞.

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...

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.

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 , ℜ ) .............................. 93. Linear functionals on L Φ ( μ , ℜ ) ....................... 264. Geometry of Fenchel-Orlicz spaces........................................ 41References....................................................................................... 54

An inequality in Orlicz function spaces with Orlicz norm

Jin Cai Wang (2003)

Commentationes Mathematicae Universitatis Carolinae

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We use Simonenko quantitative indices of an 𝒩 -function Φ to estimate two parameters q Φ and Q Φ in Orlicz function spaces L Φ [ 0 , ∞ ) with Orlicz norm, and get the following inequality: B Φ B Φ - 1 ≤ q Φ ≤ Q Φ ≤ A Φ A φ - 1 , where A Φ and B Φ are Simonenko indices. A similar inequality is obtained in L Φ [ 0 , 1 ] with Orlicz norm.