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Enclosure results for second-order relative spectra by elementary means
Author(s):
Peter
Otte
Journal:
Proc. Amer. Math. Soc.
132
(2004),
827-830.
MSC (2000):
Primary 47A10, 47B15
Posted:
July 28, 2003
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Abstract:
Motivated by the general approach due to Shargorodsky we derive enclosure results for the second-order relative spectrum of bounded selfadjoint operators by studying quadratic operator pencils. The quality of the results is discussed by means of a simple example.
References:
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- 1.
- E. B. Davies, Spectral enclosures and complex resonances for general self-adjoint operators, LMS J. Comput. Math. 1 (1998), 42-74. MR 2000e:47043
- 2.
- J. S. Howland, The Livsic matrix in perturbation theory, J. Math. Anal. Appl. 50 (1975), 415-437.MR 51:11153
- 3.
- T. Kato, Perturbation theory for linear operators, Second edition, Grundlehren der Mathematischen Wissenschaften, Band 132, Springer-Verlag, Berlin-New York, 1976. MR 53:11389
- 4.
- R. Kress, Linear integral equations, Second edition, Applied Mathematical Sciences 82, Springer-Verlag, New York, 1999.MR 2000h:45001
- 5.
- E. Shargorodsky, Geometry of higher order relative spectra and projection methods, J. Operator Theory 44 (2000), no. 1, 43-62. MR 2001f:47004
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Additional Information:
Peter
Otte
Affiliation:
Mathematisches Institut, Universität München, Theresienstraß{}e 39, 80333 München, Germany
Address at time of publication:
Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstrasse 150, 44780 Bochum, Germany
Email:
otte@mathematik.uni-muenchen.de, Peter.Otte@ruhr-uni-bochum.de
DOI:
10.1090/S0002-9939-03-07125-9
PII:
S 0002-9939(03)07125-9
Received by editor(s):
October 17, 2002
Received by editor(s) in revised form:
November 1, 2002
Posted:
July 28, 2003
Additional Notes:
I would like to thank H. Kalf for encouraging me to prepare this note
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2003,
American Mathematical Society
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