Spectral projectors of a class of non-self-adjoint operators (Q1070505)

The purpose of this paper is to study the spectral projections and the convergence of spectral expansion for a perturbed operator \(H=H_ 0+V\) on a separable Hilbert space; \(H_ 0\) is selfadjoint and \(V=WBW\) where B is an arbitrary linear bounded operator and \(W=W^*.\) Three types of spectral projections are considered, allowing the separation of ''bad parts'' of H. An estimation of \(\| E_{\lambda}- E^ 0_{\lambda}\|\), where \(E^ 0_{\lambda}\) are the spectral projections of \(H_ 0\), is also obtained. The restrictions imposed on W have a local character and may be easily verified for differential operators of Schrödinger type or related ones. The other restrictions concern the unperturbed operator \(H_ 0\).