Approximation of nonessential spectrum of transfer operators
نویسنده
چکیده
We give suucient 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 nite rank) operators L j = (Id ? j)L(Id ? j), where Id ? 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 the formulas ess (L) = lim m!1 (limsup j!1 (inf)k j L m k) 1=m = lim m!1 (limsup j!1 (inf)kL m j k) 1=m ; for the essential spectral radius 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).
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