| Title: | Extreme points of the Besicovitch--Orlicz space of almost periodic functions equipped with the Luxemburg norm (English) | 
| Author: | Hassaine, Slimane | 
| Author: | Boulahia, Fatiha | 
| Language: | English | 
| Journal: | Commentationes Mathematicae Universitatis Carolinae | 
| ISSN: | 0010-2628 (print) | 
| ISSN: | 1213-7243 (online) | 
| Volume: | 62 | 
| Issue: | 1 | 
| Year: | 2021 | 
| Pages: | 67-79 | 
| Summary lang: | English | 
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| Category: | math | 
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| Summary: | 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. (English) | 
| Keyword: | Besicovitch--Orlicz space | 
| Keyword: | extreme point | 
| Keyword: | strict convexity | 
| Keyword: | almost periodic function | 
| MSC: | 39A24 | 
| MSC: | 46B20 | 
| MSC: | 46E30 | 
| idZBL: | Zbl 07396211 | 
| idMR: | MR4270467 | 
| DOI: | 10.14712/1213-7243.2021.007 | 
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| Date available: | 2021-07-26T11:11:47Z | 
| Last updated: | 2023-04-03 | 
| Stable URL: | http://hdl.handle.net/10338.dmlcz/148939 | 
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| Reference: | [1] Bedouhene F., Morsli M., Smaali M.: On some equivalent geometric properties in the Besicovitch–Orlicz space of almost periodic functions with Luxemburg norm.Comment. Math. Univ. Carolin. 51 (2010), no. 1, 25–35. MR 2666078 | 
| Reference: | [2] Besicovitch A. S.: Almost Periodic Functions.Dover Publications, New York, 1955. Zbl 0065.07102, MR 0068029 | 
| Reference: | [3] Boulahia F., Morsli M.: Uniform non-squareness and property $(\beta)$ of Besicovitch–Orlicz spaces of almost periodic functions with Orlicz norm.Comment. Math. Univ. Carolin. 51 (2010), no. 3, 417–426. MR 2741874 | 
| Reference: | [4] Chen S.: Geometry of Orlicz spaces.Dissertationes Math. (Rozprawy Mat.) 356 (1996), 204 pages. Zbl 1089.46500, MR 1410390 | 
| Reference: | [5] Diestel J.: Geometry of Banach Spaces---Selected Topics.Lecture Notes in Mathematics, 485, Springer, Berlin, 1975. MR 0461094, 10.1007/BFb0082079 | 
| Reference: | [6] Foralewski P., Hudzik H., Płuciennik R.: Orlicz spaces without extreme points.J. Math. Anal. Appl. 361 (2010), no. 2, 506–519. MR 2568714, 10.1016/j.jmaa.2009.07.015 | 
| Reference: | [7] Hillmann T. R.: Besicovitch–Orlicz spaces of almost periodic functions.Wiley Ser. Probab. Math. Statist. Probab. Math. Statist., Wiley, New York, 1986, pages 119–167. MR 0856581 | 
| Reference: | [8] Morsli M.: On some convexity properties of the Besicovitch–Orlicz space of almost periodic functions.Comment. Math. (Prace Mat.) 34 (1994), 137–152. MR 1325081 | 
| Reference: | [9] Morsli M.: On modular approximation property in the Besicovitch–Orlicz space of almost periodic functions.Comment. Math. Univ. Carolin. 38 (1997), no. 3, 485–496. MR 1485070 | 
| Reference: | [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. MR 2199891 | 
| Reference: | [11] Morsli M., Bedouhene F.: On the strict convexity of the Besicovitch–Orlicz space of almost periodic functions with Orlicz norm.Rev. Mat. Complut. 16 (2003), no. 2, 399–415. MR 2032925, 10.5209/rev_REMA.2003.v16.n2.16812 | 
| Reference: | [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. MR 2720027 | 
| Reference: | [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. MR 3518965 | 
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