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Reflexive Orlicz spaces have uniformly normal structure

Shutao Chen; Huiying Sun — 1994

Studia Mathematica

We prove that an Orlicz space equipped with the Luxemburg norm has uniformly normal structure if and only if it is reflexive.

λ-Properties of Orlicz sequence spaces

Shutao Chen; Huiying Sun — 1994

Annales Polonici Mathematici

It is proved that every Orlicz sequence space has the λ-property. Criteria for the uniform λ-property in Orlicz sequence spaces, with Luxemburg norm and Orlicz norm, are given.

Jung constants of Orlicz function spaces.

Zhongdao Ren; Shutao Chen — 1997

Collectanea Mathematica

Estimation of the Jung constants of Orlicz function spaces equipped with either Luxemburg norm or Orlicz norm is given. The exact values of the Jung constants of a class of reflexive Orlicz function spaces have been found by using a new quantitative index of N-functions.

On weak topology of Orlicz spaces.

Shutao Chen; Huiying Sun — 1993

Collectanea Mathematica

This paper presents some properties of singular functionals on Orlicz spaces, from which criteria for weak convergence and weak compactness in such spaces are obtained.

Normal structure and weakly normal structure of Orlicz spaces

Shutao Chen; Yanzheng Duan — 1991

Commentationes Mathematicae Universitatis Carolinae

Every Orlicz space equipped with Orlicz norm has weak sum property, therefore, it has weakly normal structure and fixed point property. A criterion of sum property also of normal structure for such spaces is given as well, which shows that every Orlicz space has isonormal structure.

Extreme compact operators from Orlicz spaces to $C (Ω)$

Shutao Chen; Marek Wisła — 1993

Commentationes Mathematicae Universitatis Carolinae

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 $T : E^{ϕ} (μ) \to C (Ω)$ is extreme if and only if $T^{*} ω \in Ext B ({(E^{ϕ} (μ))}^{*})$ 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 set of extreme...

A note on Schroeder-Bernstein Property and Primary Property of Orlicz function spaces

Yanzheng Duan; Shutao Chen — 1998

Commentationes Mathematicae Universitatis Carolinae

It is shown in the note that every reflexive Orlicz function space has the Schroeder-Bernstein Property and the Primary Property.

Geometry of Orlicz spaces

Chen Shutao — 1996

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