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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A correction to ``Adjugates in Banach algebras''


Author: R. M. Brits
Journal: Proc. Amer. Math. Soc. 138 (2010), 3021-3024
MSC (2010): Primary 46H05, 46H10, 47A10
Published electronically: March 23, 2010
Original Article: Proc. Amer. Math. Soc. 134 (2006), 1397-1404
MathSciNet review: 2644913
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Abstract: Let $ A$ be a semisimple unital Banach algebra. We show that $ \operatorname{rank}_A(ab)=\operatorname{rank}_A(ba)$ for all $ a,b\in A$ if and only if $ \operatorname{soc}(A)$ is contained in the center of $ A$, and $ ab\in\operatorname{soc}(A)$ implies $ ba\in\operatorname{soc}(A)$ for all $ a,b\in A$. This corrects an erroneous statement in R.E. Harte and C. Hernández, Adjugates in Banach algebras, Proc. Amer. Math. Soc. 134(5) (2005), 1397-1404.


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Additional Information

R. M. Brits
Affiliation: Department of Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park, 2006, Johannesburg, South Africa
Email: rbrits@uj.ac.za

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10363-3
PII: S 0002-9939(10)10363-3
Received by editor(s): January 15, 2009
Received by editor(s) in revised form: October 16, 2009
Published electronically: March 23, 2010
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.