On spectral gaps of Markov maps

José Manuel Conde-Alonso; Javier Parcet; Éric Ricard

On spectral gaps of Markov maps

Probability 2017-02-17 v3 Classical Analysis and ODEs Functional Analysis Operator Algebras

Authors: José Manuel Conde-Alonso , Javier Parcet , Éric Ricard

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.

Keywords

Markov maps spectral gap noncommutative probability L_p spaces factorizable maps classical probability spaces

Cite

@article{arxiv.1702.00043,
  title  = {On spectral gaps of Markov maps},
  author = {José Manuel Conde-Alonso and Javier Parcet and Éric Ricard},
  journal= {arXiv preprint arXiv:1702.00043},
  year   = {2017}
}

On spectral gaps of Markov maps

Abstract

Keywords

Cite

Related papers