Best approximation in Orlicz spaces
Let X be a real Banach space and (Ω,μ) be a finite measure space and ϕ be a strictly icreasing convex continuous function on [0,∞) with ϕ(0)=0. The space Lϕ(μ,X) is the set of all measurable functions f with values in X such that ∫Ωϕ(‖c−1f(t)‖)dμ(t)<∞ for some c>0. One of the main results of t...
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| Format: | Article |
| Language: | English |
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Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000273 |
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| author | H. Al-Minawi S. Ayesh |
| author_facet | H. Al-Minawi S. Ayesh |
| author_sort | H. Al-Minawi |
| collection | DOAJ |
| description | Let X be a real Banach space and (Ω,μ) be a finite measure space and ϕ be a
strictly icreasing convex continuous function on [0,∞) with ϕ(0)=0. The space
Lϕ(μ,X) is the set of all measurable functions f with values in X such that ∫Ωϕ(‖c−1f(t)‖)dμ(t)<∞ for some c>0. One of the main results of this paper is:
For a closed subspace Y of X, Lϕ(μ,Y) is proximinal in Lϕ(μ,X) if and only if
L1(μ,Y) is proximinal in L1(μ,X)′′. As a result if Y is reflexive subspace of X,
then Lϕ(ϕ,Y)
is proximinal in Lϕ(μ,X). Other results on proximinality of subspaces
of Lϕ(μ,X) are proved. |
| format | Article |
| id | doaj-art-39b2f1c753ea44eaa0282010c643ca1a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-39b2f1c753ea44eaa0282010c643ca1a2025-02-03T01:31:51ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114224525210.1155/S0161171291000273Best approximation in Orlicz spacesH. Al-Minawi0S. Ayesh1Department of Mathematics, Kuwait University, P.O. BOX 5969, Safat 130, KuwaitDepartment of Mathematics, Kuwait University, P.O. BOX 5969, Safat 130, KuwaitLet X be a real Banach space and (Ω,μ) be a finite measure space and ϕ be a strictly icreasing convex continuous function on [0,∞) with ϕ(0)=0. The space Lϕ(μ,X) is the set of all measurable functions f with values in X such that ∫Ωϕ(‖c−1f(t)‖)dμ(t)<∞ for some c>0. One of the main results of this paper is: For a closed subspace Y of X, Lϕ(μ,Y) is proximinal in Lϕ(μ,X) if and only if L1(μ,Y) is proximinal in L1(μ,X)′′. As a result if Y is reflexive subspace of X, then Lϕ(ϕ,Y) is proximinal in Lϕ(μ,X). Other results on proximinality of subspaces of Lϕ(μ,X) are proved.http://dx.doi.org/10.1155/S0161171291000273 |
| spellingShingle | H. Al-Minawi S. Ayesh Best approximation in Orlicz spaces International Journal of Mathematics and Mathematical Sciences |
| title | Best approximation in Orlicz spaces |
| title_full | Best approximation in Orlicz spaces |
| title_fullStr | Best approximation in Orlicz spaces |
| title_full_unstemmed | Best approximation in Orlicz spaces |
| title_short | Best approximation in Orlicz spaces |
| title_sort | best approximation in orlicz spaces |
| url | http://dx.doi.org/10.1155/S0161171291000273 |
| work_keys_str_mv | AT halminawi bestapproximationinorliczspaces AT sayesh bestapproximationinorliczspaces |