| Title:
|
Sets invariant under projections onto one dimensional subspaces (English) |
| Author:
|
Fitzpatrick, Simon |
| Author:
|
Calvert, Bruce |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
2 |
| Year:
|
1991 |
| Pages:
|
227-232 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Hahn--Banach theorem implies that if $m$ is a one dimensional subspace of a t.v.s. $E$, and $B$ is a circled convex body in $E$, there is a continuous linear projection $P$ onto $m$ with $P(B)\subseteq B$. We determine the sets $B$ which have the property of being invariant under projections onto lines through $0$ subject to a weak boundedness type requirement. (English) |
| Keyword:
|
convex |
| Keyword:
|
projection |
| Keyword:
|
Hahn--Banach |
| Keyword:
|
subsets of $\Bbb R^2$ |
| MSC:
|
46A55 |
| MSC:
|
52A07 |
| MSC:
|
52A10 |
| idZBL:
|
Zbl 0756.52002 |
| idMR:
|
MR1137783 |
| . |
| Date available:
|
2008-10-09T13:12:03Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116960 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/116961 |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/118485 |
| . |
| Reference:
|
[1] Schaeffer H.H.: Topological Vector Spaces.MacMillan, N.Y., 1966. MR 0193469 |
| . |
