Let $T$ be a selfadjoint bounded operator acting in a real Hilbert space $H$, and denote by $S$ the unit sphere of $H$. Assume that $l_0$ is an isolated eigenvalue of $T$ of odd multiplicity greater than $1$. Given an arbitrary operator $B cl H o H$ of class $Csp{1}$, we prove that for any $e e 0$ sufficiently small there exists $x_e in S$ and $l_e$ near $l_0$, such that $Tx_e + e B(x_e) = l_e x_e$. 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 $l_0$ is odd cannot be removed.

Topological Persistence of the Normalized Eigenvectors of a Perturbed Selfadjoint Operator / R. Chiappinelli; M. Furi; M.P. Pera. - In: APPLIED MATHEMATICS LETTERS. - ISSN 0893-9659. - STAMPA. - 2010(2010), pp. 193-197. [10.1016/j.aml.2009.09.011]

Topological Persistence of the Normalized Eigenvectors of a Perturbed Selfadjoint Operator

FURI, MASSIMO;PERA, MARIA PATRIZIA
2010

Abstract

Let $T$ be a selfadjoint bounded operator acting in a real Hilbert space $H$, and denote by $S$ the unit sphere of $H$. Assume that $l_0$ is an isolated eigenvalue of $T$ of odd multiplicity greater than $1$. Given an arbitrary operator $B cl H o H$ of class $Csp{1}$, we prove that for any $e e 0$ sufficiently small there exists $x_e in S$ and $l_e$ near $l_0$, such that $Tx_e + e B(x_e) = l_e x_e$. 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 $l_0$ is odd cannot be removed.
2010
193
197
Goal 17: Partnerships for the goals
R. Chiappinelli; M. Furi; M.P. Pera
File in questo prodotto:
File Dimensione Formato  
Abstract of Topological persistence etc.png

Accesso chiuso

Tipologia: Altro
Licenza: DRM non definito
Dimensione 44.76 kB
Formato image/png
44.76 kB image/png   Visualizza/Apri   Richiedi una copia
Topological persistence etc.pdf

Accesso chiuso

Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: DRM non definito
Dimensione 523.47 kB
Formato Adobe PDF
523.47 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2158/387334
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 10
social impact