On a subspace perturbation problem

Authors:
Vadim Kostrykin, Konstantin A. Makarov and Alexander K. Motovilov

Journal:
Proc. Amer. Math. Soc. **131** (2003), 3469-3476

MSC (2000):
Primary 47A55, 47A15; Secondary 47B15

DOI:
https://doi.org/10.1090/S0002-9939-03-06917-X

Published electronically:
February 14, 2003

MathSciNet review:
1991758

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We discuss the problem of perturbation of spectral subspaces for linear self-adjoint operators on a separable Hilbert space. Let and be bounded self-adjoint operators. Assume that the spectrum of consists of two disjoint parts and such that . We show that the norm of the difference of the spectral projections

for and is less than one whenever either (i) or (ii) and certain assumptions on the mutual disposition of the sets and are satisfied.

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Additional Information

**Vadim Kostrykin**

Affiliation:
Fraunhofer-Institut für Lasertechnik, Steinbachstraße 15, D-52074, Aachen, Germany

Email:
kostrykin@ilt.fhg.de, kostrykin@t-online.de

**Konstantin A. Makarov**

Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211

Email:
makarov@math.missouri.edu

**Alexander K. Motovilov**

Affiliation:
Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia

Address at time of publication:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211

Email:
motovilv@thsun1.jinr.ru

DOI:
https://doi.org/10.1090/S0002-9939-03-06917-X

Keywords:
Perturbation theory,
spectral subspaces

Received by editor(s):
March 29, 2002

Received by editor(s) in revised form:
May 30, 2002

Published electronically:
February 14, 2003

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2003
by the authors