A Lower Bound on the Mixing Time of Uniformly Ergodic Markov Chains in Terms of the Spectral Radius

We give a bound on the mixing time of a uniformly ergodic, reversible Markov chain in terms of the spectral radius of the transition operator. This bound has been established previously in finite state spaces, and is widely believed to hold in general state spaces, but a proof has not been provided to our knowledge.