| Title:
|
Strict topologies and Banach-Steinhaus type theorems (English) |
| Author:
|
Nowak, Marian |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
563-568 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a completely regular Hausdorff space, $E$ a real Banach space, and let $C_b(X,E)$ be the space of all $E$-valued bounded continuous functions on $X$. We study linear operators from $C_b(X,E)$ endowed with the strict topologies $\beta_z$ $(z=\sigma,\tau,\infty,g)$ to a real Banach space $(Y,\|\cdot\|_Y)$. In particular, we derive Banach-Steinhaus type theorems for $(\beta_z,\|\cdot\|_Y)$ continuous linear operators from $C_b(X,E)$ to $Y$. Moreover, we study $\sigma$-additive and $\tau$-additive operators from $C_b(X,E)$ to $Y$. (English) |
| Keyword:
|
vector-valued continuous functions |
| Keyword:
|
strict topologies |
| Keyword:
|
locally solid topologies |
| Keyword:
|
Dini-topologies |
| Keyword:
|
strong Mackey space |
| Keyword:
|
$\sigma $-additive operators |
| Keyword:
|
$\tau $-additive operators |
| MSC:
|
46E10 |
| MSC:
|
47A70 |
| MSC:
|
47B38 |
| idZBL:
|
Zbl 1211.47018 |
| idMR:
|
MR2583133 |
| . |
| Date available:
|
2009-12-22T10:03:42Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137446 |
| . |
| Reference:
|
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| Reference:
|
[F] Fontenot R.A.: Strict topologies for vector-valued functions.Canad. J. Math. 26 (1974), 841--853. Zbl 0259.46037, MR 0348463, 10.4153/CJM-1974-079-1 |
| 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:
|
[NR] Nowak M., Rzepka A.: Locally solid topologies on spaces of vector-valued continuous functions.Comment. Math. Univ. Carolinae 43 (2002), no. 3, 473--483. Zbl 1068.46023, MR 1920522 |
| Reference:
|
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| . |
