Eugene Shargorodsky (KCL)

On the limit behaviour of second order relative spectra of self-adjoint operators

Abstract:
It is well known that the standard projection methods allow one to approximate the whole spectrum of a bounded self-adjoint operator but they often lead to spectral pollution, i.e. to spurious eigenvalues lying in the gaps of the essential spectrum. Methods using second order relative spectra are free from this problem, but they have not been proven to approximate the whole spectrum. L. Boulton (2006, 2007) has shown that second order relative spectra approximate all isolated eigenvalues of finite multiplicity. The aim of the talk is to prove that second order relative spectra do not in general approximate the whole of the essential spectrum of a bounded self-adjoint operator.