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Hypercontractivity and the logarithmic Sobolev inequality for the completely bounded norm
arXiv
Authors: Salman Beigi, Christopher King
Year
2015
Paper ID
27347
Status
Preprint
Abstract Read
~2 min
Abstract Words
63
Citations
N/A
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.
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- 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...
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