| Title:
|
Uniformly $\mu$-continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces (English) |
| Author:
|
Feledziak, Krzysztof |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
1998 |
| Pages:
|
453-468 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some class of locally solid topologies (called uniformly $\mu$-continuous) on \linebreak Köthe-Bochner spaces that are continuous with respect to some natural two-norm convergence are introduced and studied. A characterization of uniformly $\mu$-continuous topologies in terms of some family of pseudonorms is given. The finest uniformly $\mu$-continuous topology $\Cal T^\varphi_I(X)$ on the Orlicz-Bochner space $L^\varphi(X)$ is a generalized mixed topology in the sense of P. Turpin (see [11, Chapter I]). (English) |
| Keyword:
|
Orlicz spaces |
| Keyword:
|
Orlicz-Bochner spaces |
| Keyword:
|
Köthe-Bochner spaces |
| Keyword:
|
locally solid topologies |
| Keyword:
|
generalized mixed topologies |
| Keyword:
|
uniformly $\mu$-continuous topologies |
| Keyword:
|
inductive limit topologies |
| MSC:
|
46A70 |
| MSC:
|
46E30 |
| MSC:
|
46E40 |
| idZBL:
|
Zbl 0970.46015 |
| idMR:
|
MR1666774 |
| . |
| Date available:
|
2009-01-08T18:45:19Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119024 |
| . |
| Reference:
|
[1] Aliprantis C.D., Burkinshaw O.: Locally Solid Riesz Spaces.Academic Press, New York, 1978. Zbl 1043.46003, MR 0493242 |
| Reference:
|
[2] Bukhvalov A.V.: On an analytic representation of operators with abstract norm (in Russian).Izv. Vyssh. Uchebn. Zaved. 11 (1975), 21-32. MR 0470746 |
| Reference:
|
[3] Feledziak K., Nowak M.: Locally solid topologies on vector valued function spaces.Collect. Math., to appear. Zbl 0912.46028, MR 1602576 |
| Reference:
|
[4] Köthe G.: Topological Vector Spaces I.Springer-Verlag, Berlin, Heidelberg, New York, 1983. MR 0248498 |
| Reference:
|
[5] Krasnoselskii M., Rutickii Ya.B.: Convex Functions and Orlicz Spaces.P. Noordhoff Ltd., Groningen, 1961. MR 0126722 |
| Reference:
|
[6] Luxemburg W.A.: Banach Function Spaces.Delft, 1955. Zbl 0162.44701, MR 0072440 |
| Reference:
|
[7] Nowak M.: On two linear topologies on Orlicz spaces $L^{*\varphi}$, I.Comment. Math. 23 (1983), 71-84. Zbl 0602.46020, MR 0709174 |
| Reference:
|
[8] Nowak M.: Inductive limit of a sequence of balanced topological spaces in Orlicz spaces $L^{*\varphi}_E(\mu)$.Comment. Math. 25 (1985), 295-313. Zbl 0607.46021, MR 0844647 |
| Reference:
|
[9] Nowak M.: On some linear topology in Orlicz spaces $L^{*\varphi}_E(\mu)$, I.Comment. Math. 26 (1986), 51-68. MR 0857526 |
| Reference:
|
[10] Nowak M.: A generalized mixed topology on Orlicz spaces.Revista Matematica 7 (1) (1994), 27-56. Zbl 0806.46032, MR 1277329 |
| Reference:
|
[11] Turpin P.: Convexités dans les espaces vectoriels topologiques généraux.Dissertationes Math. 131 (1976), 221 pp. Zbl 0331.46001, MR 0423044 |
| Reference:
|
[12] Wiweger A.: Linear spaces with mixed topology.Studia Math. 20 (1961), 47-68. Zbl 0097.31301, MR 0133664 |
| . |
