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Non-commutative Nash inequalities

Kastoryano, Michael and Temme, Kristan (2016) Non-commutative Nash inequalities. Journal of Mathematical Physics, 57 (1). Art. No. 015217. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:20160225-134540321

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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 L_p spaces, where their relationship to Poincaré and log-Sobolev inequalities is fleshed out. We prove Nash inequalities for a number of unital reversible semigroups.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.4937382DOIArticle
http://scitation.aip.org/content/aip/journal/jmp/57/1/10.1063/1.4937382PublisherArticle
http://arxiv.org/abs/1508.02522arXivDiscussion Paper
Additional Information:© 2016 AIP Publishing LLC. Received 11 August 2015; accepted 24 November 2015; published online 16 December 2015. M.J.K. was supported by the Carlsbergfond and the Villum foundation. K.T. was supported by the Institute for Quantum Information and Matter, a NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation (Grant Nos. PHY-0803371 and PHY-1125565).
Group:Institute for Quantum Information and Matter, IQIM
Funders:
Funding AgencyGrant Number
CarlsbergfondUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-0803371
NSFPHY-1125565
Villum FoundationUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20160225-134540321
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160225-134540321
Official Citation:Non-commutative Nash inequalities Michael Kastoryano and Kristan Temme J. Math. Phys. 57, 015217 (2016); http://dx.doi.org/10.1063/1.4937382
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64768
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:25 Feb 2016 22:28
Last Modified:25 Feb 2016 22:28

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