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Transactions of the American Mathematical Society

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Perturbation of spectra and spectral subspaces


Authors: Vadim Kostrykin, K. A. Makarov and A. K. Motovilov
Journal: Trans. Amer. Math. Soc. 359 (2007), 77-89
MSC (2000): Primary 47A15, 47A55; Secondary 47B15
DOI: https://doi.org/10.1090/S0002-9947-06-03930-4
Published electronically: July 20, 2006
MathSciNet review: 2247883
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the problem of variation of spectral subspaces for linear self-adjoint operators with emphasis on the case of off-diagonal perturbations. We prove a number of new optimal results on the shift of the spectrum and obtain (sharp) estimates on the norm of the difference of two spectral projections associated with isolated parts of the spectrum of the perturbed and unperturbed operators, respectively.


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Additional Information

Vadim Kostrykin
Affiliation: Fraunhofer-Institut für Lasertechnik, Steinbachstraße 15, D-52074 Aachen, Germany
Address at time of publication: Institut für Mathematik, Technische Universität Clausthal, Erzstraße 1, D-38678 Clausthal-Zellerfeld, Germany
Email: kostrykin@ilt.fraunhofer.de, kostrykin@t-online.de

K. A. Makarov
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: makarov@math.missouri.edu

A. K. Motovilov
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Address at time of publication: Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Moscow Region, Russia
Email: motovilv@thsun1.jinr.ru

DOI: https://doi.org/10.1090/S0002-9947-06-03930-4
Received by editor(s): September 23, 2004
Published electronically: July 20, 2006
Dedicated: Dedicated to Volker Enss on the occasion of his 60th birthday
Article copyright: © Copyright 2006 V. Kostrykin, K. A. Makarov, A. K. Motovilov

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