Non-commutative Nash inequalities
Mathematical Physics
2018-03-13 v1 math.MP
Quantum Physics
Abstract
A set of functional inequalities - called Nash inequalities - are introduced and analyzed in the context of quantum Markov process mixing. The basic theory of Nash inequalities is extended to the setting of non-commutative Lp spaces, where their relationship to Poincare and log-Sobolev inequalities are fleshed out. We prove Nash inequalities for a number of unital reversible semigroups.
Cite
@article{arxiv.1508.02522,
title = {Non-commutative Nash inequalities},
author = {Michael J. Kastoryano and Kristan Temme},
journal= {arXiv preprint arXiv:1508.02522},
year = {2018}
}