On the structure of the set of best ||.||Φ-approximants

• Autorzy: Mazzone F.
• Języki publikacji: EN

Abstrakty

EN

Certain properties of Fi-approximants and || || (fi)-approximants were studied by Landers and Rogge, where || || (fi) is the Luxemburg norm. In particular, they investigated the existence of best ||.|| (fi)-approximants and the structure of the . set of best ||.||(fi)-approximants. These authors proved that the set of best ||.||(fi)-approximants of f given a Fi-closed lattice C is a lattice. In this paper we show that this result does not hold if we consider the Orlicz norm in place of the Luxemburg norm. Furthermore, we see that for a large class of functions Fi and measurable spaces the following statements are equivalent: 1) the set of all best || || (fi)-approximants to f in C is a lattice, for every Fi-closed lattice C and f L_fi. 2) (L_fi,,||.||fi) = (L_p,m||.||_p), for some m > 0 and 1 < p < oo.

Słowa kluczowe

EN

best approximation; Orlicz norm; Luxemburg norm; convergence of best approximants

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2002
• Tom: [Z] 42(1)
• Strony: 87--102
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Mazzone F.

• Universidad Nacional de Rio Cuarto, 5800-Rio Cuarto, Argentina,

Bibliografia

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• [7] M. Rao and Z. Ren, Theory of Orlicz Spaces, Marcel Dekker, 1991.
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