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On spectral gaps of Markov maps (1702.00043v3)
Published 31 Jan 2017 in math.PR, math.CA, math.FA, and math.OA
Abstract: It is shown that if a Markov map $T$ on a noncommutative probability space $\mathcal{M}$ has a spectral gap on $L_2(\mathcal{M})$, then it also has one on $L_p(\mathcal{M})$ for $1<p<\infty$. For fixed $p$, the converse also holds if $T$ is factorizable. These results are also new for classical probability spaces.
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