Spectral approximations of unbounded operators of the type "normal plus compact"

Michael Gil

doi:10.7169/facm/2014.51.1.7

Spectral approximations of unbounded operators of the type "normal plus compact"

Michael Gil

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let B be a compact operator in a Hilbert space H and S an unbounded normal one in H, having a compact resolvent. We consider operators of the form A = S+B. Numerous integrodifferential operators A can be represented in this form. The paper deals with approximations of the eigenvalues of the considered operators by the eigenvalues of the operators A_n= S + B_n(n = 1, 2,.), where B_nare n-dimensional operators. Besides, we obtain the error estimate of the approximation.

Original language	English
Pages (from-to)	133-140
Number of pages	8
Journal	Functiones et Approximatio, Commentarii Mathematici
Volume	51
Issue number	1
DOIs	https://doi.org/10.7169/facm/2014.51.1.7
State	Published - 1 May 2014

Keywords

Approximation
Eigenvalues
Hilbert space
Integro-differential operators
Linear operators
Schatten-von Neumann operators

ASJC Scopus subject areas

General Mathematics

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10.7169/facm/2014.51.1.7

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abstract = "Let B be a compact operator in a Hilbert space H and S an unbounded normal one in H, having a compact resolvent. We consider operators of the form A = S+B. Numerous integrodifferential operators A can be represented in this form. The paper deals with approximations of the eigenvalues of the considered operators by the eigenvalues of the operators An= S + Bn(n = 1, 2,.), where Bnare n-dimensional operators. Besides, we obtain the error estimate of the approximation.",

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AB - Let B be a compact operator in a Hilbert space H and S an unbounded normal one in H, having a compact resolvent. We consider operators of the form A = S+B. Numerous integrodifferential operators A can be represented in this form. The paper deals with approximations of the eigenvalues of the considered operators by the eigenvalues of the operators An= S + Bn(n = 1, 2,.), where Bnare n-dimensional operators. Besides, we obtain the error estimate of the approximation.

KW - Approximation

KW - Eigenvalues

KW - Hilbert space

KW - Integro-differential operators

KW - Linear operators

KW - Schatten-von Neumann operators

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ER -

Spectral approximations of unbounded operators of the type "normal plus compact"

Abstract

Keywords

ASJC Scopus subject areas

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