Best approximation in Orlicz spaces
Copyright policy )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 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.
- Kuwait University Kuwait
Best approximation, Chebyshev systems, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Banach space, proximinality, QA1-939, Mathematics
Best approximation, Chebyshev systems, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Banach space, proximinality, QA1-939, Mathematics
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