Opuscula Math. 35, no. 2 (2015), 161-169

Opuscula Mathematica

Simple eigenvectors of unbounded operators of the type "normal plus compact"

Michael Gil'

Abstract. The paper deals with operators of the form \(A=S+B\), where \(B\) is a compact operator in a Hilbert space \(H\) and \(S\) is an unbounded normal one in \(H\), having a compact resolvent. We consider approximations of the eigenvectors of \(A\), corresponding to simple eigenvalues by the eigenvectors of the operators \(A_n=S+B_n\) (\(n=1,2, \ldots\)), where \(B_n\) is an \(n\)-dimensional operator. In addition, we obtain the error estimate of the approximation.

Keywords: Hilbert space, linear operators, eigenvectors, approximation, integro-differential operators, Schatten-von Neumann operators.

Mathematics Subject Classification: 47A75, 47B10, 65F15.

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  • Michael Gil'
  • Ben Gurion University of the Negev, Department of Mathematics, P.O. Box 653, Beer-Sheva 84105, Israel
  • Communicated by P.A. Cojuhari.
  • Received: 2014-04-16.
  • Revised: 2014-06-07.
  • Accepted: 2014-06-07.
  • Published online: 2014-11-18.
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Cite this article as:
Michael Gil', Simple eigenvectors of unbounded operators of the type "normal plus compact", Opuscula Math. 35, no. 2 (2015), 161-169, http://dx.doi.org/10.7494/OpMath.2015.35.2.161

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