Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
locally uniform convexity; strict convexity; $H$-property; Besicovitch-Orlicz space; almost periodic functions
locally uniform convexity; strict convexity; $H$-property; Besicovitch-Orlicz space; almost periodic functions
Summary:
The paper is concerned with the characterization and comparison of some local geometric properties of the Besicovitch-Orlicz space of almost periodic functions. Namely, it is shown that local uniform convexity, $H$-property and strict convexity are all equivalent. In our approach, we first prove some metric type properties for the modular function associated to our space. These are then used to prove our main equivalence result.
References:
[1] Besicovitch A.S.: Almost Periodic Functions. Dover Publications, Inc., New York, 1955. MR 0068029 | Zbl 0065.07102
[2] Bedouhene F., Morsli M.: On the strict convexity of the Weyl-Orlicz space of almost periodic functions. Comment. Math. Prace Mat. 40 (2000), 33–47. MR 1810383
[3] Chen S.: Geometry of Orlicz spaces. Dissertationes Math. 356 (1996). MR 1410390 | Zbl 1089.46500
[4] Cui Y.A., Hudzik H., Meng C.: On some local geometry of Orlicz sequence spaces equipped the Luxemburg norm. Acta Math. Hungar. 80 (1998), no. 1–2, 143–154. DOI 10.1023/A:1006533011548 | MR 1624558
[5] Hillmann T.R.: Besicovitch-Orlicz spaces of almost periodic functions. Real and Stochastic Analysis, Wiley, New York, 1986, pp. 119–167. MR 0856581 | Zbl 0656.46020
[6] Hudzik H., Kurk W., Wisla M.: Strongly extreme points in Orlicz function spaces. J. Math. Anal. Appl. 189 (1995), 651–670. DOI 10.1006/jmaa.1995.1043 | MR 1312545
[7] Hudzik H., Pallaschke D.: On some convexiy properties of Orlicz sequece spaces. Math. Nachr. 186 (1997), 167–185. DOI 10.1002/mana.3211860110 | MR 1461219
[8] Fan K., Glicksberg I.: Some geometric properties of the spheres in a normed linear space. Duke Math. J., 25 (1958), 553–568. MR 0098976 | Zbl 0084.33101
[9] Kaminska A.: The criteria for local uniform rotundity of Orlicz spaces. Studia Math. 74 (1984), 201–215. MR 0781718 | Zbl 0573.46014
[10] Kaminska A.: On some convexity properties of Musielak-Orlicz spaces. Suppl. Rend. Circ. Mat. Palermo (2) 1984, Suppl. No. 5, 63–72. MR 0781940 | Zbl 0573.46015
[11] Megginson R.E.: An Introduction to Banach Space Theory. Graduate Texts in Mathematics, 183, Springer, New York, 1998. DOI 10.1007/978-1-4612-0603-3 | MR 1650235 | Zbl 0910.46008
[12] 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 | Zbl 0839.46012
[13] 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 | Zbl 1061.46029
[14] Morsli M., Bedouhene F.: On the uniform convexity of the Besicovitch-Orlicz space of almost periodic functions with Orlicz norm. Colloq. Math. 102 (2005), no. 1, 97–111. DOI 10.4064/cm102-1-9 | MR 2150272 | Zbl 1112.46013
[15] 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 | Zbl 0937.46009
[16] Pluciennik R., Wang T.F., Zhang Y.L.: H-point and denting points in Orlicz spaces. Comment. Math. Prace Mat. 33 (1993), 135–151. MR 1269408
Search
Partner of
