| Title:
|
Sigma order continuity and best approximation in $L_\varrho$-spaces (English) |
| Author:
|
Kilmer, Shelby J. |
| Author:
|
Kozƚowski, Wojciech M. |
| Author:
|
Lewicki, Grzegorz |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
2 |
| Year:
|
1991 |
| Pages:
|
241-250 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
best approximation |
| Keyword:
|
lattices |
| Keyword:
|
modular function spaces |
| Keyword:
|
$L_\varrho $-spaces |
| Keyword:
|
Orlicz spaces |
| MSC:
|
41A50 |
| MSC:
|
41A65 |
| MSC:
|
46E30 |
| idZBL:
|
Zbl 0754.41017 |
| idMR:
|
MR1137785 |
| . |
| Date available:
|
2008-10-09T13:12:10Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116962 |
| . |
| Reference:
|
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| Reference:
|
[2] Birnbaum Z., Orlicz W.: Über die Verallgemeinerung des Begriffes der zueinander konjugierten Potenzen.Studia Math. 3 (1931), 1-67. Zbl 0003.25202 |
| Reference:
|
[3] Kilmer S., Kozlowski W.M., Lewicki G.: Best approximants in modular function spaces.Journ. Approx. Th. 63 (1990), 338-367. Zbl 0718.41049, MR 1081035 |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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[9] Lindenstrauss J., Tzafriri J.: Classical Banach Spaces II: Function Spaces.Springer-Verlag, Berlin, Heidelberg, New York, 1979. Zbl 0403.46022, MR 0540367 |
| Reference:
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[10] Luxemburg W., Zaanen A.: Notes on Banach function spaces I-XIII.Proc. Royal Acad. Sci., Amsterdam (1963) A-66, 135-153, 239-263, 496-504, 655-681; (1964) A-64, 101-119; (1964) A-67, 360-376, 493-543. MR 0173167 |
| Reference:
|
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| Reference:
|
[12] Orlicz W.: Über eine gewisse Klasse von Räumen vom Typus B.Bull. Acad. Polon. Sci. Ser A (1932), 207-220. Zbl 0006.31503 |
| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
