On modular approximation property in the Besicovitch-Orlicz space of almost periodic functions
Morsli, Mohamed
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997), p. 485-496 / Harvested from Czech Digital Mathematics Library
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We investigate some convergence questions in the class of Besicovitch-Orlicz spaces of vector valued functions. Next, the existence problem of the projection operator on closed convex subsets is considered in the class of almost periodic functions. This problem was considered in [5], in the case of an Orlicz space. The approximation property obtained in both cases are of the same kind. However, the arguments which are used in the proofs are different.

Publié le : 1997-01-01
Classification:  42A75,  46B20,  46E40,  47B38 
@article{118947,
     author = {Mohamed Morsli},
     title = {On modular approximation property in the Besicovitch-Orlicz space of almost periodic functions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {38},
     year = {1997},
     pages = {485-496},
     zbl = {0937.46009},
     mrnumber = {1485070},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118947}
}

Morsli, Mohamed. On modular approximation property in the Besicovitch-Orlicz space of almost periodic functions. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 485-496. http://gdmltest.u-ga.fr/item/118947/

Hillmann T.R. Besicovitch-Orlicz spaces of almost periodic functions, Real and Stochastic Analysis, Wiley, 1986, pp.119-167. | MR 0856581 | Zbl 0656.46020

Hudzik H. An estimation of the modulus of convexity in a class of Orlicz spaces, Math. Japonica 32 2 (1987), 227-237. (1987) | MR 0895543 | Zbl 0637.46031

Hudzik H. Convexity in Musielak-Orlicz spaces, Hokkaido Math. J. 14 (1985), 85-96. (1985) | MR 0781829 | Zbl 0579.46023

Kaminska A. On uniform convexity of Orlicz space, Indag. Math. 44.1 (1982), 27-36. (1982) | MR 0653453

Khamsi M.; Kozlowski W.; Shutao C. Some geometrical properties and fixed point theorems in Orlicz spaces, J. of Math. and Appl., vol 155, no. 2, March 1, 1991. | MR 1097290 | Zbl 0752.46011

Morsli M. Some convexity properties of the Besicovitch-Orlicz space of almost periodic functions, Comment. Math. 34 (1994), 137-152. (1994) | MR 1325081 | Zbl 0839.46012

Morsli M. On uniform convexity of Besicovitch-Orlicz space of almost periodic functions, Functiones et Approximatio 22 (1993), 95-106. (1993) | MR 1304363

Musielak J.; Orlicz W. On modular space, Studia Math. 18 (1959), 49-65. (1959) | MR 0101487

Nakano H. Topology and Linear Topological Spaces, Tokyo, 1951. | MR 0046560