Kastoryano, Michael and Temme, Kristan (2016) Non-commutative Nash inequalities. Journal of Mathematical Physics, 57 (1). Art. No. 015217. ISSN 0022-2488. doi:10.1063/1.4937382. https://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 | ||||||||||||||
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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 | ||||||||||||||
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Issue or Number: | 1 | ||||||||||||||
DOI: | 10.1063/1.4937382 | ||||||||||||||
Record Number: | CaltechAUTHORS:20160225-134540321 | ||||||||||||||
Persistent URL: | https://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: | 10 Nov 2021 23:35 |
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