Smooth points of the unit sphere in Musielak-Orlicz function spaces equipped with the Luxemburg norm

Zenon Zbąszyniak

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 1, page 95-102
  • ISSN: 0010-2628

Abstract

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There is given a criterion for an arbitrary element from the unit sphere of Musielak-Orlicz function space equipped with the Luxemburg norm to be a point of smoothness. Next, as a corollary, a criterion of smoothness of these spaces is given.

How to cite

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Zbąszyniak, Zenon. "Smooth points of the unit sphere in Musielak-Orlicz function spaces equipped with the Luxemburg norm." Commentationes Mathematicae Universitatis Carolinae 35.1 (1994): 95-102. <http://eudml.org/doc/247572>.

@article{Zbąszyniak1994,
abstract = {There is given a criterion for an arbitrary element from the unit sphere of Musielak-Orlicz function space equipped with the Luxemburg norm to be a point of smoothness. Next, as a corollary, a criterion of smoothness of these spaces is given.},
author = {Zbąszyniak, Zenon},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Musielak-Orlicz function; Musielak-Orlicz space; support functional; smooth point; smooth space; Musielak-Orlicz space; support functional; smooth point; smooth space; Musielak-Orlicz function space; Luxemburg norm},
language = {eng},
number = {1},
pages = {95-102},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Smooth points of the unit sphere in Musielak-Orlicz function spaces equipped with the Luxemburg norm},
url = {http://eudml.org/doc/247572},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Zbąszyniak, Zenon
TI - Smooth points of the unit sphere in Musielak-Orlicz function spaces equipped with the Luxemburg norm
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 1
SP - 95
EP - 102
AB - There is given a criterion for an arbitrary element from the unit sphere of Musielak-Orlicz function space equipped with the Luxemburg norm to be a point of smoothness. Next, as a corollary, a criterion of smoothness of these spaces is given.
LA - eng
KW - Musielak-Orlicz function; Musielak-Orlicz space; support functional; smooth point; smooth space; Musielak-Orlicz space; support functional; smooth point; smooth space; Musielak-Orlicz function space; Luxemburg norm
UR - http://eudml.org/doc/247572
ER -

References

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  1. Ando T., Linear functionals on Orlicz spaces, Nieuw Arch. Wisk. 3,8 (1960), 1-16. (1960) Zbl0129.08001MR0123907
  2. Chen S., Smoothness of Orlicz spaces, Comment. Math. (Prace Matem.) 27,1 (1987), 49-58. (1987) Zbl0641.46010MR0910960
  3. Diestel J., Geometry of Banach spaces - selected topics, Lecture Notes in Math. 481, Springer-Verlag, 1975. Zbl0466.46021MR0461094
  4. Grzaslewicz R., Hudzik H., Smooth points of Orlicz spaces equipped with the Luxemburg norm, Math. Nachrichten 155 (1992), 31-45. (1992) MR1231254
  5. Himmelberg C.J., Measurable relations, Fund. Math. 87,1 (1975), 53-72. (1975) Zbl0296.28003MR0367142
  6. Hudzik H., On some equivalent conditions in Musielak-Orlicz spaces, Comment. Math. (Prace Matem.) 24,1 (1984), 57-64. (1984) Zbl0564.46022MR0759055
  7. Hudzik H., Ye Y., Support functionals and smoothness in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm, Comment. Math. Univ. Carolinae 31,4 (1990), 661-684. (1990) Zbl0721.46012MR1091364
  8. Kamińska A., Some convexity properties of Musielak-Orlicz spaces of Bochner type, Supplemento ai Rendiconti del Circolo Mathematico di Palermo, Serie II 10 (1985), 63-73. (1985) MR0894273
  9. Kozek A., Convex integral functionals on Orlicz spaces, Comment. Math. (Prace Matem.) 21,1 (1980), 109-135. (1980) MR0577677
  10. Krasnoselskiĭ M.A., Rutickiĭ Ya.B., Convex functions and Orlicz spaces, Groningen 1961 (translation). 
  11. Luxemburg W.A.J., Banach function spaces, Thesis, Delft 1955. Zbl0162.44701MR0072440
  12. Musielak J., Orlicz spaces and modular spaces, Lecture Notes in Math. 1034, Springer-Verlag 1983. Zbl0557.46020MR0724434
  13. Nowak M., Linear functionals on Orlicz sequence spaces without local convexity, Internat. J. of Math. and Math. Sciences 1992. Zbl0784.46009MR1155516
  14. Phelps R., Convex functions, monotone operators and differentiability, Lecture Notes in Math. 1364, Springer-Verlag, 1989. Zbl0921.46039MR0984602
  15. Pluciennik R., Ye Y., Differentiability of Musielak-Orlicz sequence spaces, Comment. Math. Univ. Carolinae 30 (1989), 699-711. (1989) Zbl0706.46022MR1045898
  16. Rao M.M., Ren Z.D., Theory of Orlicz spaces, Marcel Dekker Inc., New York-Basel-Hong Kong, 1991. Zbl0724.46032MR1113700

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