2000 character limit reached
Hypercontractivity and the logarithmic Sobolev inequality for the completely bounded norm (1509.02610v3)
Published 9 Sep 2015 in math-ph, math.FA, math.MP, and quant-ph
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 $q$ to be deduced from LS at $q=2$.