| Title:
|
Stability of positive part of unit ball in Orlicz spaces (English) |
| Author:
|
Grząślewicz, Ryszard |
| Author:
|
Seredyński, Witold |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
413-424 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this paper is to investigate the stability of the positive part of the unit ball in Orlicz spaces, endowed with the Luxemburg norm. The convex set $Q$ in a topological vector space is stable if the midpoint map $\Phi\colon Q\times Q\rightarrow Q$, $\Phi(x,y) =(x+y)/2$ is open with respect to the inherited topology in $Q$. The main theorem is established: In the Orlicz space $L^\varphi(\mu)$ the stability of the positive part of the unit ball is equivalent to the stability of the unit ball. (English) |
| Keyword:
|
stable convex set |
| MSC:
|
46Axx |
| MSC:
|
46B20 |
| MSC:
|
46Cxx |
| MSC:
|
46E30 |
| MSC:
|
52A41 |
| idZBL:
|
Zbl 1121.52001 |
| idMR:
|
MR2174521 |
| . |
| Date available:
|
2009-05-05T16:52:09Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119537 |
| . |
| Reference:
|
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| . |
