Sigma order continuity and best approximation in L ϱ -spaces

Shelby J. Kilmer; Wojciech M. Kozƚowski; Grzegorz Lewicki

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 2, page 241-250
  • ISSN: 0010-2628

Abstract

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In this paper we give a characterization of σ -order continuity of modular function spaces L ϱ in terms of the existence of best approximants by elements of order closed sublattices of L ϱ . 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.

How to cite

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Kilmer, Shelby J., Kozƚowski, Wojciech M., and Lewicki, Grzegorz. "Sigma order continuity and best approximation in $L_\varrho $-spaces." Commentationes Mathematicae Universitatis Carolinae 32.2 (1991): 241-250. <http://eudml.org/doc/247255>.

@article{Kilmer1991,
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.},
author = {Kilmer, Shelby J., Kozƚowski, Wojciech M., Lewicki, Grzegorz},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {best approximation; lattices; modular function spaces; $L_\varrho $-spaces; Orlicz spaces; -order continuity; modular function space; closed sublattices; Musielak-Orlicz spaces},
language = {eng},
number = {2},
pages = {241-250},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Sigma order continuity and best approximation in $L_\varrho $-spaces},
url = {http://eudml.org/doc/247255},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Kilmer, Shelby J.
AU - Kozƚowski, Wojciech M.
AU - Lewicki, Grzegorz
TI - Sigma order continuity and best approximation in $L_\varrho $-spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 2
SP - 241
EP - 250
AB - 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.
LA - eng
KW - best approximation; lattices; modular function spaces; $L_\varrho $-spaces; Orlicz spaces; -order continuity; modular function space; closed sublattices; Musielak-Orlicz spaces
UR - http://eudml.org/doc/247255
ER -

References

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