  In the first part of this paper, we give a useful criterion for uniform
integrability of exponential martingales in the context of Markov processes.
The condition of this criterion is easy to verify and is, in general, much
weaker than the commonly used Novikov's condition. In the second part of this
paper, we present a new approach to the study of spectral bounds of Feynman-Kac
semigroups for a large class of symmetric Markov processes. We first establish
criteria for the $L^p$-independence of spectral bounds for Feynman-Kac
semigroups generated by continuous additive functionals, using gaugeability
results obtained by the author in \cite{C}. We then extend these analytic
criteria for the $L^p$-independence of spectral bounds to non-local Feynman-Kac
semigroups via pure jump Girsanov transforms. For this, the uniform
integrability of the exponential martingales established in the first part of
this paper plays an important role. We use it to show that Kato classes
introduced in \cite{C} can only become larger under pure jump Girsanov
transforms with symmetric jumping functions.
