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

 

Inner bounds for the spectrum of quasinormal operators


Author: M. I. Gil'
Journal: Proc. Amer. Math. Soc. 131 (2003), 3737-3746
MSC (2000): Primary 47A55, 47A75; Secondary 47G10, 47G20
Published electronically: February 20, 2003
MathSciNet review: 1998181
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Abstract: A linear operator in a separable Hilbert space is called a quasinormal one if it is a sum of a normal operator and a compact one. In the paper, bounds for the spectrum of quasinormal operators are established. In addition, the lower estimate for the spectral radius is derived. Under some restrictions, that estimate improves the well-known results. Applications to integral operators and matrices are discussed. Our results are new even in the finite-dimensional case.


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Additional Information

M. I. Gil'
Affiliation: Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
Email: gilmi@black.bgu.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06950-8
PII: S 0002-9939(03)06950-8
Keywords: Linear operators, spectrum, spectral radius, integral operators, finite and infinite matrices
Received by editor(s): March 21, 2001
Received by editor(s) in revised form: June 24, 2002
Published electronically: February 20, 2003
Additional Notes: This research was supported by the Israel Ministry of Science and Technology
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society