On spectral gaps of Markov maps

José Conde-Alonso (1) , Javier Parcet (2) , Éric Ricard (3)

1 UAB - Universitat Autònoma de Barcelona = Autonomous University of Barcelona = Universidad Autónoma de Barcelona
2 CSIC - Consejo Superior de Investigaciones Cientificas [España] = Spanish National Research Council [Spain]
3 LMNO - Laboratoire de Mathématiques Nicolas Oresme

It is shown that if a Markov map T on a noncommutative probability space M has a spectral gap on L2(M), then it also has one on Lp(M) for 1 < p < ∞. For fixed p, the converse also holds if T is factorizable. Some results are also new for classical probability spaces.

Domaines: Analyse fonctionnelle [math.FA]

José Conde-Alonso, Javier Parcet, Éric Ricard. On spectral gaps of Markov maps. Israel Journal of Mathematics, 2018, 226 (1), pp.189 - 203. ⟨10.1007/s11856-018-1693-1⟩. ⟨hal-01876527⟩