On extreme points of Orlicz spaces with Orlicz norm.

Henryk Hudzik; Marek Wisla

Collectanea Mathematica (1993)

  • Volume: 44, Issue: 1-2-3, page 135-146
  • ISSN: 0010-0757

Abstract

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In the paper we consider a class of Orlicz spaces equipped with the Orlicz norm over a non-negative, complete and sigma-finite measure space (T,Sigma,mu), which covers, among others, Orlicz spaces isomorphic to L-infinite and the interpolation space L1 + L-infinite. We give some necessary conditions for a point x from the unit sphere to be extreme. Applying this characterization, in the case of an atomless measure mu, we find a description of the set of extreme points of L1 + L-infinite which corresponds with the result obtained by R. Graslewicz and H. Schaefer [3] and H. Schaefer [13].

How to cite

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Hudzik, Henryk, and Wisla, Marek. "On extreme points of Orlicz spaces with Orlicz norm.." Collectanea Mathematica 44.1-2-3 (1993): 135-146. <http://eudml.org/doc/42034>.

@article{Hudzik1993,
abstract = {In the paper we consider a class of Orlicz spaces equipped with the Orlicz norm over a non-negative, complete and sigma-finite measure space (T,Sigma,mu), which covers, among others, Orlicz spaces isomorphic to L-infinite and the interpolation space L1 + L-infinite. We give some necessary conditions for a point x from the unit sphere to be extreme. Applying this characterization, in the case of an atomless measure mu, we find a description of the set of extreme points of L1 + L-infinite which corresponds with the result obtained by R. Graslewicz and H. Schaefer [3] and H. Schaefer [13].},
author = {Hudzik, Henryk, Wisla, Marek},
journal = {Collectanea Mathematica},
keywords = {Espacio de Orlicz; Funciones convexas; Bola unidad; Interpolación; Operadores lineales; Orlicz spaces equipped with the Orlicz norm},
language = {eng},
number = {1-2-3},
pages = {135-146},
title = {On extreme points of Orlicz spaces with Orlicz norm.},
url = {http://eudml.org/doc/42034},
volume = {44},
year = {1993},
}

TY - JOUR
AU - Hudzik, Henryk
AU - Wisla, Marek
TI - On extreme points of Orlicz spaces with Orlicz norm.
JO - Collectanea Mathematica
PY - 1993
VL - 44
IS - 1-2-3
SP - 135
EP - 146
AB - In the paper we consider a class of Orlicz spaces equipped with the Orlicz norm over a non-negative, complete and sigma-finite measure space (T,Sigma,mu), which covers, among others, Orlicz spaces isomorphic to L-infinite and the interpolation space L1 + L-infinite. We give some necessary conditions for a point x from the unit sphere to be extreme. Applying this characterization, in the case of an atomless measure mu, we find a description of the set of extreme points of L1 + L-infinite which corresponds with the result obtained by R. Graslewicz and H. Schaefer [3] and H. Schaefer [13].
LA - eng
KW - Espacio de Orlicz; Funciones convexas; Bola unidad; Interpolación; Operadores lineales; Orlicz spaces equipped with the Orlicz norm
UR - http://eudml.org/doc/42034
ER -

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