| Title:
|
On modular approximation property in the Besicovitch-Orlicz space of almost periodic functions (English) |
| Author:
|
Morsli, Mohamed |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
485-496 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
modular approximation |
| Keyword:
|
Besicovitch-Orlicz space |
| Keyword:
|
almost periodic functions |
| MSC:
|
42A75 |
| MSC:
|
46B20 |
| MSC:
|
46E40 |
| MSC:
|
47B38 |
| idZBL:
|
Zbl 0937.46009 |
| idMR:
|
MR1485070 |
| . |
| Date available:
|
2009-01-08T18:35:39Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118947 |
| . |
| Reference:
|
[1] Hillmann T.R.: Besicovitch-Orlicz spaces of almost periodic functions.Real and Stochastic Analysis, Wiley, 1986, pp.119-167. Zbl 0656.46020, MR 0856581 |
| Reference:
|
[2] Hudzik H.: An estimation of the modulus of convexity in a class of Orlicz spaces.Math. Japonica 32 2 (1987), 227-237. Zbl 0637.46031, MR 0895543 |
| Reference:
|
[3] Hudzik H.: Convexity in Musielak-Orlicz spaces.Hokkaido Math. J. 14 (1985), 85-96. Zbl 0579.46023, MR 0781829 |
| Reference:
|
[4] Kaminska A.: On uniform convexity of Orlicz space.Indag. Math. 44.1 (1982), 27-36. MR 0653453 |
| Reference:
|
[5] 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. Zbl 0752.46011, MR 1097290 |
| Reference:
|
[6] Morsli M.: Some convexity properties of the Besicovitch-Orlicz space of almost periodic functions.Comment. Math. 34 (1994), 137-152. Zbl 0839.46012, MR 1325081 |
| Reference:
|
[7] Morsli M.: On uniform convexity of Besicovitch-Orlicz space of almost periodic functions.Functiones et Approximatio 22 (1993), 95-106. MR 1304363 |
| Reference:
|
[8] Musielak J., Orlicz W.: On modular space.Studia Math. 18 (1959), 49-65. MR 0101487 |
| Reference:
|
[9] Nakano H.: Topology and Linear Topological Spaces.Tokyo, 1951. MR 0046560 |
| . |
