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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:
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


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