Some spectral properties of m-accretive differential operators (Q1119884)

Spectral properties of a second order differential operator D perturbed by a potential q are studied. In the first theorem the author gives conditions on the coefficients of D and on q implying that the operator \(T=D+q\), acting in \(L_ 2\), is m-accretive and the resolvent \((z-T)^{- 1}\) is compact. In the second theorem he gives conditions implying that the operator \((z-D)^{-1}-(z-T)^{-1}\) is compact, from which it follows the equality of the essential spectra \(\sigma_ e(D)=\sigma_ e(T)\).