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arXiv · 1508.02522

Non-commutative Nash inequalities

Michael J. Kastoryano·Kristan Temme
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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 Lp spaces, where their relationship to Poincare and log-Sobolev inequalities are fleshed out. We prove Nash inequalities for a number of unital reversible semigroups.

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Michael J. Kastoryano, Kristan Temme. 2015-08-11. Non-commutative Nash inequalities. https://doi.org/10.1063/1.4937382

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