Abstract
In this paper we give a characterization of σ-order continuity of modular function spaces L% in terms of the existence of best approximants by elements of order closed sublattices of L%. We consider separately the case of Musielak–Orlicz spaces generated by non-σ-finite measures. Such spaces are not modular function spaces and the proofs require somewhat different methods.
Department(s)
Mathematics
Document Type
Article
Keywords
best approximation, lattices, modular function spaces, L%-spaces, Orlicz space
Publication Date
7-30-1990
Recommended Citation
Kilmer, Shelby J., Wojciech M. Kozlowski, and Grzegorz Lewicki. "Best approximants in modular function spaces." Journal of Approximation Theory 63, no. 3 (1990): 338-367.
Journal Title
Comment.Math.Univ.Carolinae
COinS
