| Title:
|
Topological dual of non-locally convex Orlicz-Bochner spaces (English) |
| Author:
|
Nowak, Marian |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
511-529 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $L^\varphi (X)$ be an Orlicz-Bochner space defined by an Orlicz function $\varphi $ taking only finite values (not necessarily convex) over a $\sigma $-finite atomless measure space. It is proved that the topological dual $L^\varphi (X)^*$ of $L^\varphi (X)$ can be represented in the form: $L^\varphi (X)^*=L^\varphi (X)^\sim _n\oplus L^\varphi (X)^\sim _s$, where $L^\varphi (X)^\sim_n$ and $L^\varphi (X)^\sim_s$ denote the order continuous dual and the singular dual of $L^\varphi (X)$ respectively. The spaces $L^\varphi (X)^*$, $L^\varphi (X)^\sim _n$ and $L^\varphi (X)^\sim _s$ are examined by means of the H. Nakano's theory of conjugate modulars. (Studia Mathematica 31 (1968), 439--449). The well known results of the duality theory of Orlicz spaces are extended to the vector-valued setting. (English) |
| Keyword:
|
vector-valued function spaces |
| Keyword:
|
Orlicz functions |
| Keyword:
|
Orlicz spaces |
| Keyword:
|
Orlicz-Bochner spaces |
| Keyword:
|
topological dual |
| Keyword:
|
order dual |
| Keyword:
|
order continuous linear functionals |
| Keyword:
|
singular linear functionals |
| Keyword:
|
modulars |
| Keyword:
|
conjugate modulars |
| MSC:
|
46A20 |
| MSC:
|
46E30 |
| MSC:
|
46E40 |
| idZBL:
|
Zbl 1010.46028 |
| idMR:
|
MR1732484 |
| . |
| Date available:
|
2009-01-08T18:54:44Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119107 |
| . |
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