Spectral permanence for the Moore-Penrose inverse

Authors:
Dragan S. Djordjević, Snežana Č. Živković-Zlatanović and Robin E. Harte

Journal:
Proc. Amer. Math. Soc. **140** (2012), 3237-3245

MSC (2000):
Primary 46H05, 47A05, 47A53

Published electronically:
January 26, 2012

MathSciNet review:
2917096

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: C* algebra ``spectral permanence'' extends from the ordinary inverse to the Moore-Penrose inverse.

**1.**S. R. Caradus, W. E. Pfaffenberger, and Bertram Yood,*Calkin algebras and algebras of operators on Banach spaces*, Marcel Dekker, Inc., New York, 1974. Lecture Notes in Pure and Applied Mathematics, Vol. 9. MR**0415345****2.**D. S. Djordjević, J. J. Koliha, and I. Straškraba,*Factorization of EP elements in 𝐶*-algebras*, Linear Multilinear Algebra**57**(2009), no. 6, 587–594. MR**2543720**, 10.1080/03081080802264372**3.**Dragan S. Djordjević and Vladimir Rakočević,*Lectures on generalized inverses*, University of Niš, Faculty of Sciences and Mathematics, Niš, 2008. MR**2472376****4.**Robin Harte,*Invertibility and singularity for bounded linear operators*, Monographs and Textbooks in Pure and Applied Mathematics, vol. 109, Marcel Dekker, Inc., New York, 1988. MR**920812****5.**Robin Harte and Mostafa Mbekhta,*On generalized inverses in 𝐶*-algebras*, Studia Math.**103**(1992), no. 1, 71–77. MR**1184103****6.**Robin Harte and Mícheál Ó Searcóid,*Positive elements and the 𝐵* condition*, Math. Z.**193**(1986), no. 1, 1–9. MR**852905**, 10.1007/BF01163350**7.**J. J. Koliha,*A generalized Drazin inverse*, Glasgow Math. J.**38**(1996), no. 3, 367–381. MR**1417366**, 10.1017/S0017089500031803**8.**Xavier Mary,*On the converse of a theorem of R. Harte and M. Mbekhta: Erratum to: “On generalized inverses in 𝐶*-algebras” [Studia Math. 103 (1992), no. 1, 71–77; MR1184103]*, Studia Math.**184**(2008), no. 2, 149–151. MR**2365807**, 10.4064/sm184-2-4**9.**M. Takesaki,*Theory of operator algebras. I*, Encyclopaedia of Mathematical Sciences, vol. 124, Springer-Verlag, Berlin, 2002. Reprint of the first (1979) edition; Operator Algebras and Non-commutative Geometry, 5. MR**1873025**

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Additional Information

**Dragan S. Djordjević**

Affiliation:
Department of Mathematics and Informatics, Faculty of Sciences and Mathematics, University of Niš, Niš 18000, Serbia

Email:
dragan@pmf.ni.ac.rs; dragandjordjevic70@gmail.com

**Snežana Č. Živković-Zlatanović**

Affiliation:
Department of Mathematics and Informatics, Faculty of Sciences and Mathematics, University of Niš, Niš 18000, Serbia

Email:
mladvlad@open.telekom.rs

**Robin E. Harte**

Affiliation:
School of Mathematics, Trinity College, Dublin 2, Ireland

Email:
rharte@maths.tcd.ie

DOI:
https://doi.org/10.1090/S0002-9939-2012-11159-1

Keywords:
Drazin inverse,
Moore-Penrose inverse,
Fredholm theory,
C* algebras

Received by editor(s):
July 9, 2010

Received by editor(s) in revised form:
March 30, 2011

Published electronically:
January 26, 2012

Additional Notes:
The authors are supported by the Ministry of Science of Serbia, grant #174007.

Communicated by:
Marius Junge

Article copyright:
© Copyright 2012
American Mathematical Society