Best approximation in Orlicz spaces

H. Al-Minawi and S. Ayesh

International Journal of Mathematics and Mathematical Sciences, 1991, vol. 14, 1-8

Abstract:

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 L ϕ ( μ , X ) is the set of all measurable functions f with values in X such that ∫ Ω ϕ ( ‖ c − 1 f ( t ) ‖ ) d μ ( t ) < ∞ for some c > 0 . One of the main results of this paper is: For a closed subspace Y of X , L ϕ ( μ , Y ) is proximinal in L ϕ ( μ , X ) if and only if L 1 ( μ , Y ) is proximinal in L 1 ( μ , X ) ′ ​ ′ . As a result if Y is reflexive subspace of X , then L ϕ ( ϕ , Y ) is proximinal in L ϕ ( μ , X ) . Other results on proximinality of subspaces of L ϕ ( μ , X ) are proved.

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:629390

DOI: 10.1155/S0161171291000273

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