| Title:
|
Sets invariant under projections onto two 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:
|
233-239 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Blaschke--Kakutani result characterizes inner product spaces $E$, among normed spaces of dimension at least 3, by the property that for every 2 dimensional subspace $F$ there is a norm 1 linear projection onto $F$. In this paper, we determine which closed neighborhoods $B$ of zero in a real locally convex space $E$ of dimension at least 3 have the property that for every 2 dimensional subspace $F$ there is a continuous linear projection $P$ onto $F$ with $P(B)\subseteq B$. (English) |
| Keyword:
|
inner product space |
| Keyword:
|
two dimensional subspace |
| Keyword:
|
projection |
| MSC:
|
46A03 |
| MSC:
|
46A55 |
| MSC:
|
46C05 |
| MSC:
|
46C15 |
| MSC:
|
52A07 |
| MSC:
|
52A15 |
| idZBL:
|
Zbl 0756.46010 |
| idMR:
|
MR1137784 |
| . |
| Date available:
|
2008-10-09T13:12:06Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116961 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/116960 |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/118485 |
| . |
| Reference:
|
[1] Amir D.: Characterizations of Inner Product Spaces.Birkhäuser Verlag, Basel, Boston, Stuttgart, 1986. Zbl 0617.46030, MR 0897527 |
| Reference:
|
[2] Calvert B., Fitzpatrick S.: Nonexpansive projections onto two dimensional subspaces of Banach spaces.Bull. Aust. Math. Soc. 37 (1988), 149-160. Zbl 0634.46013, MR 0926986 |
| Reference:
|
[3] Fitzpatrick S., Calvert B.: Sets invariant under projections onto one dimensional subspaces.Comment. Math. Univ. Carolinae 32 (1991), 227-232. Zbl 0756.52002, MR 1137783 |
| . |
