| Title:
|
Support functionals and smoothness in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm (English) |
| Author:
|
Hudzik, Henryk |
| Author:
|
Ye, Yi Ning |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
31 |
| Issue:
|
4 |
| Year:
|
1990 |
| Pages:
|
661-684 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Musielak-Orlicz spaces |
| Keyword:
|
support functionals |
| Keyword:
|
smoothness |
| MSC:
|
46A45 |
| MSC:
|
46B20 |
| MSC:
|
46B25 |
| MSC:
|
46B45 |
| idZBL:
|
Zbl 0721.46012 |
| idMR:
|
MR1091364 |
| . |
| Date available:
|
2008-06-05T21:45:53Z |
| Last updated:
|
2012-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/106902 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/118655 |
| . |
| Reference:
|
[1] Ando T.: Linear functionals on Orlicz spaces.Nieuw Arch. Wisk. 3, 8 (1960), 1-16. Zbl 0129.08001, MR 0123907 |
| Reference:
|
[2] Chen S.: Smoothness of Orlicz spaces.Comment. Math. (Prace Mat.) 27, 1 (1987), 49-58. Zbl 0641.46010, MR 0910960 |
| Reference:
|
[3] Diestel J.: Geometry of Banach spaces-selected topics.Lecture Notes in Math. 481, Springer-Verlag, 1975. Zbl 0307.46009, MR 0461094 |
| Reference:
|
[4] Grzaslewicz R., Hudzik H.: Smooth points of Orlicz spaces equipped with the Luxemburg norm.(to appear). MR 1231254 |
| Reference:
|
[5] Kaminska A.: Flat Orlicz-Musielak sequence spaces.Bull. Acad. Polon. Sci. Math. 30, 7-8 (1982), 347-352. Zbl 0513.46008, MR 0707748 |
| Reference:
|
[6] Krasnoselskii M. A., Rutickii Ya. B.: Convex function and Orlicz spaces.Groningen 1961 (translation). |
| Reference:
|
[7] Luxemburg W. A. J.: Banach function spaces.Thesis, Delf 1955. Zbl 0068.09204, MR 0072440 |
| Reference:
|
[8] Musielak J.: Orlicz spaces and modular spaces.Lecture Notes in Math. 1034, Springer-Verlag, 1983. Zbl 0557.46020, MR 0724434 |
| Reference:
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[9] Nowak M.: Linear funciionals on Orlicz sequence spacers without local convexity.(to appear). MR 1155516 |
| Reference:
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[10] Phelps R.: Convex functions, monotone operators and differentiability.Lecture Notes in Math. 1364, Springer-Verlag, 1989. Zbl 0658.46035, MR 0984602 |
| Reference:
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[11] Pluciennik R., Ye Y.: Differentiability of Musielak-Orlicz sequence spaces.Comment. Math. Univ. Carolinae 30 (1989), 699-711. Zbl 0706.46022, MR 1045898 |
| Reference:
|
[12] Rao M. M.: Smoothness of Orlicz spaces I.Indagationes Math., Ser. A 27 (1965), 671-680. Zbl 0132.09104, MR 0190704 |
| Reference:
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[13] Rao M. M.: Smoothness of Orlicz spaces II.Indagationes Math., Ser. A 27 (1965), 681-690. MR 0190704 |
| Reference:
|
[14] Ye Y.: Differentiability of Orlicz space.Journal of Harbin University of Science and Technology 2 (1987), 114-118 (in Chinese). Zbl 0653.46029 |
| Reference:
|
[15] Wu C, Wang T., Chen S., Wang Yu.: Geometry of Orlicz spaces.Harbin 1986 (in Chinese). |
| . |
