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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

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

Author(s): 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 | References | Similar articles | Additional information

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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K. Jörgens, Linear Integral Operators, Pitman, Boston, 1982. MR83j:45001

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T. Palmer, Banach Algebras and the General Theory of $*$-Algebras, Vol. I, Encyclopedia of Math. and its Appl., Vol. 49, Cambridge Univ. Press, Cambridge, 1994. MR 95c:46002

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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: 10.1090/S0002-9939-98-04218-X
PII: S 0002-9939(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
Copyright of article: Copyright 1998, American Mathematical Society




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