Equivalence of exponential ergodicity and L2-exponential convergence for Markov chains

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Eigenvalues, inequalities and ergodic theory (2001, background): “oes there exist any relation between the above inequalities and the traditional three types of ergodicity? 6 EIGENVALUES, INEQUALITIES AND ERGODIC THEORY 3.3 New picture of ergodictheory Theorem[16] ,[19][20]. For reversible Markov chains, we have the following diagram: Nash inequality ււ ցց Log. So”
Essential spectral radius for Markov semigroups (I): discrete time case (2004, background): “By Riesz-Thorin’s theorem, ress(P |Lp(µ) ) 3 ] obtains this spectral gap in L 2 (µ) in the context of Theorem 1.3 in sev-”
Average optimality for continuous-time Markov decision processes in polish spaces (2006, methodology): “tial convergence rate ρ and the constant R in (3.3) are independent of all stationary policies. On the other hand, other examples and approaches that yield exponential ergodicity (3.3) can be seen in [3, 7, 28, 36, 40], for instance. Finally, be warned that all of the underlying processes in this pa”