Opuscula Math. 35, no. 2 (2015), 161-169
http://dx.doi.org/10.7494/OpMath.2015.35.2.161

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.
• Revised: 2014-06-07.
• Accepted: 2014-06-07.
• Published online: 2014-11-18.