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EnglishLet 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.
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http://hdl.handle.net/11365/21090| Titolo: | Topological persistence of the normalized eigenvectors of a perturbed self-adjoint operator |
| Autori: | |
| Anno: | 2010 |
| Rivista: | |
| 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. |
| Handle: | http://hdl.handle.net/11365/21090 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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