$$L^p$$-independence of spectral radius for generalized Feynman–Kac semigroups

Abstract

Under mild conditions on measures used in the perturbation, we establish the $$L^p$$ -independence of spectral radius for generalized Feynman–Kac semigroups without assuming the irreducibility and the boundedness of the function appeared in the continuous additive functionals locally of zero energy in the framework of symmetric Markov processes. These results are obtained by using the gaugeability approach developed by the first named author as well as the recent progress on the irreducible decomposition for Markov processes proved by the third author and on the analytic characterizations of gaugeability for generalized Feynman–Kac functionals developed by the second and third authors.