Sigma order continuity and best approximation in $L_\varrho$-spaces
Kilmer, Shelby J. ; Kozƚowski, Wojciech M. ; Lewicki, Grzegorz
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991), p. 241-250 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1991-01-01
Classification:  41A50,  41A65,  46E30 
@article{116962,
     author = {Shelby J. Kilmer and Wojciech M. Kozlowski and Grzegorz Lewicki},
     title = {Sigma order continuity and best approximation in $L\_\varrho$-spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {32},
     year = {1991},
     pages = {241-250},
     zbl = {0754.41017},
     mrnumber = {1137785},
     language = {en},
     url = {http://dml.mathdoc.fr/item/116962}
}

Kilmer, Shelby J.; Kozƚowski, Wojciech M.; Lewicki, Grzegorz. Sigma order continuity and best approximation in $L_\varrho$-spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 241-250. http://gdmltest.u-ga.fr/item/116962/

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