| Title:
|
Integral representations of the $g$-Drazin inverse in $C^*$-algebras (English) |
| Author:
|
González, N. Castro |
| Author:
|
Koliha, J. J. |
| Author:
|
Wei, Yimin |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
129 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
71-77 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper gives new integral representations of the $g$-Drazin inverse of an element $a$ of a $C^*$-algebra that require no restriction on the spectrum of $a$. The representations involve powers of $a$ and of its adjoint. (English) |
| Keyword:
|
$C^*$-algebra |
| Keyword:
|
$g$-Drazin inverse |
| Keyword:
|
integral representation |
| MSC:
|
46H05 |
| MSC:
|
46L05 |
| MSC:
|
47A05 |
| idZBL:
|
Zbl 1056.46048 |
| idMR:
|
MR2048787 |
| DOI:
|
10.21136/MB.2004.134109 |
| . |
| Date available:
|
2009-09-24T22:12:42Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134109 |
| . |
| Reference:
|
[1] N. Castro González, J. J. Koliha: Perturbation of the Drazin inverse for closed linear operators.Integral Equations Operator Theory 36 (2000), 92–106. MR 1736919, 10.1007/BF01236288 |
| Reference:
|
[2] N. Castro González, J. J. Koliha, Yimin Wei: On integral representation of the Drazin inverse in Banach algebras.Proc. Edinburgh Math. Soc. 45 (2002), 327–331. MR 1912642 |
| Reference:
|
[3] M. P. Drazin: Pseudo-inverse in associative rings and semigroups.Amer. Math. Monthly 65 (1958), 506–514. MR 0098762, 10.2307/2308576 |
| Reference:
|
[4] J. J. Koliha: A generalized Drazin inverse.Glasgow Math. J. 38 (1996), 367–381. Zbl 0897.47002, MR 1417366, 10.1017/S0017089500031803 |
| Reference:
|
[5] J. J. Koliha: Isolated spectral points.Proc. Amer. Math. Soc. 124 (1996), 3417–4324. Zbl 0864.46028, MR 1342031, 10.1090/S0002-9939-96-03449-1 |
| Reference:
|
[6] J. J. Koliha: The Drazin and Moore-Penrose inverse in $C^*$-algebras.Math. Proc. Roy. Irish Acad. 99A (1999), 17–27. Zbl 0943.46031, MR 1883060 |
| Reference:
|
[7] J. J. Koliha, I. Straškraba: Power bounded and exponentially bounded matrices.Appl. Math. 44 (1999), 289–308. MR 1698770, 10.1023/A:1023032629988 |
| Reference:
|
[8] D. Showalter: Representation and computation of the pseudoinverse.Proc. Amer. Math. Soc. 18 (1967), 584–586. Zbl 0148.38205, MR 0212594, 10.1090/S0002-9939-1967-0212594-0 |
| . |
