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Elements of rings with equal spectral idempotents

Part of: Selfadjoint operator algebras Basic linear algebra Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  09 April 2009

J. J. Koliha  and
Pedro Patricio
J. J. Koliha
Affiliation:
Department of Mathematics and Statistics, University of Melbourne, VIC 3010, Australia e-mail: [email protected]
Pedro Patricio
Affiliation:
CMAT—Centro de Matemática, Universidade do Minho, 4710-057 Braga, Portugal e-mail: [email protected]
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Abstract

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In this paper we define and study a generalized Drazin inverse xD for ring elements x, and give a characterization of elements a, b for which aaD = bbD. We apply our results to the study of EP elements in a ring with involution.

Keywords

associative ringinvolutionidempotentDrazin inverseMoore–Penrose inverseEP element

MSC classification

Secondary: 15A09: Matrix inversion, generalized inverses 46H05: General theory of topological algebras 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 72 , Issue 1 , February 2002 , pp. 137 - 152
Copyright
Copyright © Australian Mathematical Society 2002

References

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