| Title:
|
A new relationship between decomposability and convexity (English) |
| Author:
|
Satco, Bianca |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
457-466 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present work we prove that, in the space of Pettis integrable functions, any subset that is decomposable and closed with respect to the topology induced by the so-called Alexiewicz norm $\left| \left\|\cdot \right\| \right|$ \big(where $\left| \left\| f\right\| \right| =\sup_{[a,b] \subset [0,1]} \big\| \int_{a}^{b}f(s) ds \big\|$\big) is convex. As a consequence, any such family of Pettis integrable functions is also weakly closed. (English) |
| Keyword:
|
Pettis integral |
| Keyword:
|
decomposable set |
| Keyword:
|
convex set |
| Keyword:
|
Alexiewicz norm |
| MSC:
|
28B05 |
| MSC:
|
46A20 |
| MSC:
|
46A55 |
| MSC:
|
46E30 |
| MSC:
|
46E40 |
| MSC:
|
46G10 |
| MSC:
|
52A07 |
| MSC:
|
54A10 |
| idZBL:
|
Zbl 1150.46325 |
| idMR:
|
MR2281007 |
| . |
| Date available:
|
2009-05-05T16:58:38Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119606 |
| . |
| Reference:
|
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| . |
