Extreme points of the Besicovitch--Orlicz space of almost periodic functions equipped with the Luxemburg norm

Slimane Hassaine; Fatiha Boulahia

Commentationes Mathematicae Universitatis Carolinae (2021)

  • Issue: 1, page 67-79
  • ISSN: 0010-2628

Abstract

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We investigate which points in the unit sphere of the Besicovitch--Orlicz space of almost periodic functions, equipped with the Luxemburg norm, are extreme points. Sufficient conditions for the strict convexity of this space are also given.

How to cite

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Hassaine, Slimane, and Boulahia, Fatiha. "Extreme points of the Besicovitch--Orlicz space of almost periodic functions equipped with the Luxemburg norm." Commentationes Mathematicae Universitatis Carolinae (2021): 67-79. <http://eudml.org/doc/297632>.

@article{Hassaine2021,
abstract = {We investigate which points in the unit sphere of the Besicovitch--Orlicz space of almost periodic functions, equipped with the Luxemburg norm, are extreme points. Sufficient conditions for the strict convexity of this space are also given.},
author = {Hassaine, Slimane, Boulahia, Fatiha},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Besicovitch--Orlicz space; extreme point; strict convexity; almost periodic function},
language = {eng},
number = {1},
pages = {67-79},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Extreme points of the Besicovitch--Orlicz space of almost periodic functions equipped with the Luxemburg norm},
url = {http://eudml.org/doc/297632},
year = {2021},
}

TY - JOUR
AU - Hassaine, Slimane
AU - Boulahia, Fatiha
TI - Extreme points of the Besicovitch--Orlicz space of almost periodic functions equipped with the Luxemburg norm
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2021
PB - Charles University in Prague, Faculty of Mathematics and Physics
IS - 1
SP - 67
EP - 79
AB - We investigate which points in the unit sphere of the Besicovitch--Orlicz space of almost periodic functions, equipped with the Luxemburg norm, are extreme points. Sufficient conditions for the strict convexity of this space are also given.
LA - eng
KW - Besicovitch--Orlicz space; extreme point; strict convexity; almost periodic function
UR - http://eudml.org/doc/297632
ER -

References

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  10. Morsli M., Boulahia F., Uniformly non- l n 1 Besicovitch–Orlicz space of almost periodic functions, Comment. Math. (Prace Mat.) 45 (2005), no. 1, 25–34. MR2199891
  11. Morsli M., Bedouhene F., 10.5209/rev_REMA.2003.v16.n2.16812, Rev. Mat. Complut. 16 (2003), no. 2, 399–415. MR2032925DOI10.5209/rev_REMA.2003.v16.n2.16812
  12. Shang S., Cui Y., Fu Y., Extreme points and rotundity in Musielak–Orlicz–Bochner function spaces endowed with Orlicz norm, Abstr. Appl. Anal. 2010 (2010), Art. ID 914183, 13 pages. MR2720027
  13. Wisła M., Geometric properties of Orlicz spaces equipped with p -Amemiya norms—results and open questions, Comment. Math. 55 (2015), no. 2, 183–209. MR3518965

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