Approximation of nonessential spectrum of transfer operators

Abstract

We give sufficient conditions to approximate the `nonessential' spectrum of a bounded operator acting on a Banach space by part of the spectra of a sequence of compact (or finite rank) operators , where is a suitable family of uniformly bounded operators which approach the identity. (By nonessential spectrum we mean here all the spectrum outside of the disc of radius equal to the essential spectral radius.) For this, we combine the formulae