| Title:
|
Strong topologies on vector-valued function spaces (English) |
| Author:
|
Nowak, Marian |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
2 |
| Year:
|
2000 |
| Pages:
|
401-414 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(X,\Vert \cdot \Vert _X)$ be a real Banach space and let $E$ be an ideal of $L^0$ over a $\sigma $-finite measure space $(Ø,\Sigma ,\mu )$. Let $(X)$ be the space of all strongly $\Sigma $-measurable functions $f\: Ø\rightarrow X$ such that the scalar function ${\widetilde{f}}$, defined by ${\widetilde{f}}(ø)=\Vert f(ø)\Vert _X$ for $ø\in Ø$, belongs to $E$. The paper deals with strong topologies on $E(X)$. In particular, the strong topology $\beta (E(X), E(X)^\sim _n)$ ($E(X)^\sim _n=$ the order continuous dual of $E(X)$) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies. (English) |
| Keyword:
|
vector valued function spaces |
| Keyword:
|
locally solid topologies |
| Keyword:
|
strong topologies |
| Keyword:
|
Mackey topologies |
| Keyword:
|
absolute weak topologies |
| MSC:
|
46A40 |
| MSC:
|
46E30 |
| MSC:
|
46E40 |
| idZBL:
|
Zbl 1050.46513 |
| idMR:
|
MR1761397 |
| . |
| Date available:
|
2009-09-24T10:34:00Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127579 |
| . |
| Reference:
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