Hypercontractivity and the logarithmic Sobolev inequality for the completely bounded norm
Mathematical Physics
2015-11-09 v3 Functional Analysis
math.MP
Quantum Physics
Abstract
We develop the notions of hypercontractivity (HC) and the log-Sobolev (LS) inequality for completely bounded norms of one-parameter semigroups of super-operators acting on matrix algebras. We prove the equivalence of the completely bounded versions of HC and LS under suitable hypotheses. We also prove a version of the Gross Lemma which allows LS at general to be deduced from LS at .
Cite
@article{arxiv.1509.02610,
title = {Hypercontractivity and the logarithmic Sobolev inequality for the completely bounded norm},
author = {Salman Beigi and Christopher King},
journal= {arXiv preprint arXiv:1509.02610},
year = {2015}
}
Comments
27 pages, V3 minor changes