| Title:
|
Duality theory of spaces of vector-valued continuous functions (English) |
| Author:
|
Nowak, Marian |
| Author:
|
Rzepka, Aleksandra |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
55-73 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a completely regular Hausdorff space, $E$ a real normed space, and let $C_b(X,E)$ be the space of all bounded continuous $E$-valued functions on $X$. We develop the general duality theory of the space $C_b(X,E)$ endowed with locally solid topologies; in particular with the strict topologies $\beta_z(X,E)$ for $z=\sigma, \tau, t$. As an application, we consider criteria for relative weak-star compactness in the spaces of vector measures $M_z(X,E')$ for $z=\sigma, \tau, t$. It is shown that if a subset $H$ of $M_z(X,E')$ is relatively $\sigma(M_z(X,E'), C_b(X,E))$-compact, then the set $\operatorname{conv} (S(H))$ is still relatively $\sigma(M_z(X,E'), C_b(X,E))$-compact ($S(H)=$ the solid hull of $H$ in $M_z(X,E')$). A Mackey-Arens type theorem for locally convex-solid topologies on $C_b(X,E)$ is obtained. (English) |
| Keyword:
|
vector-valued continuous functions |
| Keyword:
|
strict topologies |
| Keyword:
|
locally solid topologies |
| Keyword:
|
weak-star compactness |
| Keyword:
|
vector measures |
| MSC:
|
46E10 |
| MSC:
|
46E15 |
| MSC:
|
46E40 |
| MSC:
|
46G10 |
| idZBL:
|
Zbl 1123.46021 |
| idMR:
|
MR2175859 |
| . |
| Date available:
|
2009-05-05T16:49:35Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119508 |
| . |
| Reference:
|
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| . |
