We consider a class of Ruelle type operators which play an important role in the study of singular perturbation of symbolic dynamics via thermodynamic formalism. We study the eigenvalues of those operators with maximal modulus and obtain necessary and suffcient conditions for them to be semisimple.
"Spectral properties of a class of generalized Ruelle operators." Hiroshima Math. J. 39 (2) 181 - 205, July 2009. https://doi.org/10.32917/hmj/1249046336