Let T be a self-adjoint bounded operator acting in a real Hilbert space H, and denote by S the unit sphere of H. Assume that is an isolated eigenvalue of T of odd multiplicity greater than 1. Given an arbitrary operator B:H ! H of class C1, we prove that for any sufficiently small there exists such that Tx" C "B.x". This result was conjectured, but not proved, in a previous article by the authors.We provide an example showing that the assumption that the multiplicity of 0 is odd cannot be removed.

Chiappinelli, R., Furi, M., & Pera, M.P. (2010). Topological persistence of the normalized eigenvectors of a perturbed self-adjoint operator. APPLIED MATHEMATICS LETTERS, 23(2), 193-197 [10.1016/j.aml.2009.09.011].

Topological persistence of the normalized eigenvectors of a perturbed self-adjoint operator

CHIAPPINELLI, RAFFAELE;
2010

Abstract

Let T be a self-adjoint bounded operator acting in a real Hilbert space H, and denote by S the unit sphere of H. Assume that is an isolated eigenvalue of T of odd multiplicity greater than 1. Given an arbitrary operator B:H ! H of class C1, we prove that for any sufficiently small there exists such that Tx" C "B.x". This result was conjectured, but not proved, in a previous article by the authors.We provide an example showing that the assumption that the multiplicity of 0 is odd cannot be removed.
Chiappinelli, R., Furi, M., & Pera, M.P. (2010). Topological persistence of the normalized eigenvectors of a perturbed self-adjoint operator. APPLIED MATHEMATICS LETTERS, 23(2), 193-197 [10.1016/j.aml.2009.09.011].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/21090
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