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Common operator properties
of the linear operators $RS$ and $SR$


Author: Bruce A. Barnes
Journal: Proc. Amer. Math. Soc. 126 (1998), 1055-1061
MSC (1991): Primary 47A10, 47A60, 47B30
MathSciNet review: 1443814
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Abstract: Let $S$ and $R$ be bounded linear operators defined on Banach spaces, $S\colon X\to Y$, $R\colon Y\to X$. When $\lambda \neq 0$, then the operators $\lambda -SR$ and $\lambda -RS$ have many basic operator properties in common. This situation is studied in this paper.


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Additional Information

Bruce A. Barnes
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: barnes@math.uoregon.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04218-X
Keywords: Spectrum, closed range, Fredholm operator, poles of the resolvent
Received by editor(s): February 22, 1996
Received by editor(s) in revised form: September 23, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society