V. Baladi and M. Holschneider
Approximation of the nonessential spectrum of transfer operators
(52K, AMS TeX)
ABSTRACT. We give sufficient conditions to approximate the ``nonessential''
spectrum of a bounded operator L acting on a Banach
space B by part of the spectra of a sequence of compact
(or finite rank) operators L_j=(I-P_j) L (I-P_j),
where $I-P_j 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 formulas for the essential
spectral radius in terms of the P_j with nonstandard
perturbative results on the stability of the nonessential
spectrum of quasicompact operators.
We present concrete applications to transfer operators of smooth
expanding maps using multiresolution analysis
(large scale approximation projections).