Functiones et Approximatio Commentarii Mathematici

Spectral approximations of unbounded operators of the type ``Normal Plus Compact''

Michael Gil'

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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 integro-differential 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 $B_n$ are $n$-dimensional operators. Besides, we obtain the error estimate of the approximation.

Article information

Funct. Approx. Comment. Math., Volume 51, Number 1 (2014), 133-140.

First available in Project Euclid: 24 September 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A75: Eigenvalue problems [See also 47J10, 49R05]
Secondary: 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20] 47B99: None of the above, but in this section

Hilbert space linear operators eigenvalues approximation integro-differential operators Schatten-von Neumann operators


Gil', Michael. Spectral approximations of unbounded operators of the type ``Normal Plus Compact''. Funct. Approx. Comment. Math. 51 (2014), no. 1, 133--140. doi:10.7169/facm/2014.51.1.7.

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