CONTENTSPreface..............................................................................................................................4Introduction........................................................................................................................51. Orlicz spaces..................................................................................................................6 1.1. Orlicz functions...........................................................................................................6 1.2....
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We prove that an Orlicz space equipped with the Luxemburg norm has uniformly normal structure if and only if it is reflexive.
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.
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.
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.
It is shown in the note that every reflexive Orlicz function space has the Schroeder-Bernstein Property and the Primary Property.
Let be the subspace of finite elements of an Orlicz space endowed with the Luxemburg norm. The main theorem says that a compact linear operator is extreme if and only if on a dense subset of , where is a compact Hausdorff topological space and . This is done via the description of the extreme points of the space of continuous functions , 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...
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.
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