Support functionals and smoothness in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm

Henryk Hudzik; Yi Ning Ye

Commentationes Mathematicae Universitatis Carolinae (1990)

  • Volume: 031, Issue: 4, page 661-684
  • ISSN: 0010-2628

Abstract

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Support functionals in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm are completely characterized. An explicit formula for regular support functionals is given. For obtaining a characterization of singular support functionals a generalized Banach limit is applied. Some necessary and sufficient conditions for smooothness of these spaces are given, too.

How to cite

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Hudzik, Henryk, and Ye, Yi Ning. "Support functionals and smoothness in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm." Commentationes Mathematicae Universitatis Carolinae 031.4 (1990): 661-684. <http://eudml.org/doc/17888>.

@article{Hudzik1990,
abstract = {Support functionals in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm are completely characterized. An explicit formula for regular support functionals is given. For obtaining a characterization of singular support functionals a generalized Banach limit is applied. Some necessary and sufficient conditions for smooothness of these spaces are given, too.},
author = {Hudzik, Henryk, Ye, Yi Ning},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Musielak-Orlicz spaces; support functionals; smoothness; Support functionals in Musiełak-Orlicz sequence spaces endowed with the Luxemburg norm; regular support functionals; singular support functionals; generalized Banach limit; smoothness},
language = {eng},
number = {4},
pages = {661-684},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Support functionals and smoothness in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm},
url = {http://eudml.org/doc/17888},
volume = {031},
year = {1990},
}

TY - JOUR
AU - Hudzik, Henryk
AU - Ye, Yi Ning
TI - Support functionals and smoothness in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1990
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 031
IS - 4
SP - 661
EP - 684
AB - Support functionals in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm are completely characterized. An explicit formula for regular support functionals is given. For obtaining a characterization of singular support functionals a generalized Banach limit is applied. Some necessary and sufficient conditions for smooothness of these spaces are given, too.
LA - eng
KW - Musielak-Orlicz spaces; support functionals; smoothness; Support functionals in Musiełak-Orlicz sequence spaces endowed with the Luxemburg norm; regular support functionals; singular support functionals; generalized Banach limit; smoothness
UR - http://eudml.org/doc/17888
ER -

References

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  2. Chen S., Smoothness of Orlicz spaces, Comment. Math. (Prace Mat.) 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. (1975) Zbl0307.46009MR0461094
  4. Grzaslewicz R., Hudzik H., Smooth points of Orlicz spaces equipped with the Luxemburg norm, (to appear). MR1231254
  5. Kaminska A., Flat Orlicz-Musielak sequence spaces, Bull. Acad. Polon. Sci. Math. 30, 7-8 (1982), 347-352. (1982) Zbl0513.46008MR0707748
  6. Krasnoselskii M. A., Rutickii Ya. B., Convex function and Orlicz spaces, Groningen 1961 (translation). (1961) 
  7. Luxemburg W. A. J., Banach function spaces, Thesis, Delf 1955. (1955) Zbl0068.09204MR0072440
  8. Musielak J., Orlicz spaces and modular spaces, Lecture Notes in Math. 1034, Springer-Verlag, 1983. (1983) Zbl0557.46020MR0724434
  9. Nowak M., Linear funciionals on Orlicz sequence spacers without local convexity, (to appear). MR1155516
  10. Phelps R., Convex functions, monotone operators and differentiability, Lecture Notes in Math. 1364, Springer-Verlag, 1989. (1989) Zbl0658.46035MR0984602
  11. Pluciennik R., Ye Y., Differentiability of Musielak-Orlicz sequence spaces, Comment. Math. Univ. Carolinae 30 (1989), 699-711. (1989) Zbl0706.46022MR1045898
  12. Rao M. M., Smoothness of Orlicz spaces I, Indagationes Math., Ser. A 27 (1965), 671-680. (1965) Zbl0132.09104MR0190704
  13. Rao M. M., Smoothness of Orlicz spaces II, Indagationes Math., Ser. A 27 (1965), 681-690. (1965) MR0190704
  14. Ye Y., Differentiability of Orlicz space, Journal of Harbin University of Science and Technology 2 (1987), 114-118 (in Chinese). (1987) Zbl0653.46029
  15. Wu C, Wang T., Chen S., Wang Yu., Geometry of Orlicz spaces, Harbin 1986 (in Chinese). (1986) 

Citations in EuDML Documents

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  1. Henryk Hudzik, Yi Ning Ye, Correction to the paper: Support functionals and smoothness in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm
  2. Henryk Hudzik, Zenon Zbąszyniak, Smooth points of Musielak-Orlicz sequence spaces equipped with the Luxemburg norm
  3. Harold Bevan Thompson, Yunan Cui, The fixed point property in Musielak-Orlicz sequence spaces
  4. Ghassan Alherk, Henryk Hudzik, Copies of l 1 and c o in Musielak-Orlicz sequence spaces
  5. Yunan Cui, Henryk Hudzik, Ryszard Płuciennik, Banach-Saks property in some Banach sequence spaces
  6. Henryk Hudzik, L. Wang, Ting Fu Wang, Smooth, very smooth and strongly smooth points in Musielak-Orlicz function spaces equipped with the Luxemburg norm
  7. Zenon Zbąszyniak, Smooth points of the unit sphere in Musielak-Orlicz function spaces equipped with the Luxemburg norm

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