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
DOI:
https://doi.org/10.1090/S0002-9939-2012-11159-1
Published electronically:
January 26, 2012
MathSciNet review:
2917096
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: C* algebra “spectral permanence” extends from the ordinary inverse to the Moore-Penrose inverse.
- 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
- D. S. Djordjević, J. J. Koliha, and I. Straškraba, Factorization of EP elements in $C^\ast $-algebras, Linear Multilinear Algebra 57 (2009), no. 6, 587–594. MR 2543720, DOI https://doi.org/10.1080/03081080802264372
- Dragan S. Djordjević and Vladimir Rakočević, Lectures on generalized inverses, University of Niš, Faculty of Sciences and Mathematics, Niš, 2008. MR 2472376
- 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
- Robin Harte and Mostafa Mbekhta, On generalized inverses in $C^*$-algebras, Studia Math. 103 (1992), no. 1, 71–77. MR 1184103, DOI https://doi.org/10.4064/sm-103-1-71-77
- Robin Harte and Mícheál Ó Searcóid, Positive elements and the $B^\ast $ condition, Math. Z. 193 (1986), no. 1, 1–9. MR 852905, DOI https://doi.org/10.1007/BF01163350
- J. J. Koliha, A generalized Drazin inverse, Glasgow Math. J. 38 (1996), no. 3, 367–381. MR 1417366, DOI https://doi.org/10.1017/S0017089500031803
- Xavier Mary, On the converse of a theorem of R. Harte and M. Mbekhta: Erratum to: “On generalized inverses in $C^\ast $-algebras” [Studia Math. 103 (1992), no. 1, 71–77; MR1184103], Studia Math. 184 (2008), no. 2, 149–151. MR 2365807, DOI https://doi.org/10.4064/sm184-2-4
- 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
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46H05, 47A05, 47A53
Retrieve articles in all journals with MSC (2000): 46H05, 47A05, 47A53
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
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
