| Title:
|
On product of projections (English) |
| Author:
|
Moslehian, Mohammad Sal |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
40 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
355-357 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An operator with infinite dimensional kernel is positive iff it is a positive scalar times a certain product of three projections. (English) |
| Keyword:
|
projection |
| Keyword:
|
positive operator |
| Keyword:
|
factorization |
| MSC:
|
47A05 |
| MSC:
|
47A68 |
| MSC:
|
47B15 |
| idZBL:
|
Zbl 1109.47302 |
| idMR:
|
MR2129957 |
| . |
| Date available:
|
2008-06-06T22:44:20Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107919 |
| . |
| Reference:
|
[1] Fong C. K., Wu P. Y.: Diagonal operators: dilation, sum and product.Acta Sci. Math. (Szeged) 57 (1993), No. 1-4, 125–138. Zbl 0819.47047, MR 1243273 |
| Reference:
|
[2] Halmos P. R.: Products of shifts.Duke Math. J. 39 (1972), 779–787. Zbl 0254.47038, MR 0313860 |
| Reference:
|
[3] Halmos P. R., Kakutani S.: Products of symmetries.Bull. Amer. Math. Soc. 64 (1958), 77–78. Zbl 0084.10602, MR 0100225 |
| Reference:
|
[4] Hawkins J. B., Kammerer W. J.: A class of linear transformations which can be written as the product of projections.Proc. Amer. Math. Soc. 19 (1968), 739–745. MR 0225195 |
| Reference:
|
[5] Phillips N. C.: Every invertible Hilbert space operator is a product of seven positive operators.Canad. Math. Bull. 38 (1995), no. 2, 230–236. Zbl 0826.46049, MR 1335103 |
| Reference:
|
[6] Radjavi H.: On self-adjoint factorization of operators.Canad. J. Math. 21 (1969), 1421–1426. Zbl 0188.44301, MR 0251575 |
| Reference:
|
[7] Radjavi H.: Products of hermitian matrices and symmetries.Proc. Amer. Math. Soc. 21 (1969), 369–372; 26 (1970), 701. Zbl 0175.30703, MR 0240116 |
| Reference:
|
[8] Wu P. Y.: Product of normal operators.Canad. J. Math. XL, No 6 (1988), 1322–1330. MR 0990101 |
| Reference:
|
[9] Wu P. Y.: The operator factorization problems.Lin. Appl. 117 (1989), 35–63. Zbl 0673.47018, MR 0993030 |
| . |
