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

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 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.