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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |