Shelby J. Kilmer, Wojciech M. Kozlowski, Grzegorz Lewicki
Sigma order continuity and best approximation in $L_\varrho $-spaces

Comment.Math.Univ.Carolinae 32,2 (1991) 241-250.

Abstract:In this paper we give a characterization of $\sigma $-order continuity of modular function spaces $L_\varrho $ in terms of the existence of best approximants by elements of order closed sublattices of $L_\varrho $. We consider separately the case of Musielak--Orlicz spaces generated by non-$\sigma $-finite measures. Such spaces are not modular function spaces and the proofs require somewhat different methods.

Keywords: best approximation, lattices, modular function spaces, $L_\varrho $-spaces, Orlicz spaces
AMS Subject Classification: Primary 46E30, 41A50