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Extension of the best approximation operator in Orlicz spaces. (English) Zbl 1160.41308

The authors study an extension of the best approximation operator from an Orlicz space \(L^\phi\) to \(L^{\phi'}\).

MSC:

41A35 Approximation by operators (in particular, by integral operators)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47B38 Linear operators on function spaces (general)
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References:

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[2] D. Landers and L. Rogge, “Isotonic approximation in Ls,” Journal of Approximation Theory, vol. 31, no. 3, pp. 199-223, 1981. · Zbl 0467.41014
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[8] H. D. Brunk and S. Johansen, “A generalized Radon-Nikodym derivative,” Pacific Journal of Mathematics, vol. 34, pp. 585-617, 1970. · Zbl 0183.48302
[9] F. Mazzone and H. Cuenya, “A characterization of best \varphi -approximants with applications to multidimensional isotonic approximation,” Constructive Approximation, vol. 21, no. 2, pp. 207-223, 2005. · Zbl 1067.41014
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