| Title:
|
Inductive limit topologies on Orlicz spaces (English) |
| Author:
|
Nowak, Marian |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
667-675 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $L^\varphi $ be an Orlicz space defined by a convex Orlicz function $\varphi $ and let $E^\varphi $ be the space of finite elements in $L^\varphi $ (= the ideal of all elements of order continuous norm). We show that the usual norm topology $\Cal T_\varphi$ on $L^\varphi $ restricted to $E^\varphi $ can be obtained as an inductive limit topology with respect to some family of other Orlicz spaces. As an application we obtain a characterization of continuity of linear operators defined on $E^\varphi $. (English) |
| Keyword:
|
Orlicz spaces |
| Keyword:
|
inductive limit topologies |
| Keyword:
|
convex functions |
| MSC:
|
46A13 |
| MSC:
|
46E30 |
| MSC:
|
54A10 |
| idZBL:
|
Zbl 0756.46014 |
| idMR:
|
MR1159813 |
| . |
| Date available:
|
2009-01-08T17:48:01Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118446 |
| . |
| 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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| Reference:
|
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| Reference:
|
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| Reference:
|
[9] Nowak M.: Some equalities among Orlicz spaces I.Comment. Math. 29 (1990), 255-275. Zbl 0742.46014, MR 1059131 |
| Reference:
|
[10] Robertson A.P., Robertson W.J.: Topological Vector Spaces.Cambridge, 1973. Zbl 0423.46001, MR 0350361 |
| Reference:
|
[11] Turpin Ph.: Convexités dans les espaces vectoriels topologiques généraux.Dissertationes Math. 131 (1976). Zbl 0331.46001, MR 0423044 |
| Reference:
|
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| . |
