L ^p-independence of spectral bounds of generalized non-local Feynman-Kac semigroups

Let X be a symmetric strong Markov process on a Luzin space. In this paper, we present criteria of the L ^p-independence of spectral bounds for generalized non-local Feynman-Kac semigroups of X that involve continuous additive functionals of X having zero quadratic variations and discontinuous additive functionals of X.