$L^p$-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 $X$.