Simple eigenvectors of unbounded operators of the type “normal plus compact”
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.