Quasi-states and the Poisson bracket on surfaces

Frol Zapolsky

doi:10.3934/jmd.2007.1.465

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2007, Volume 1, Issue 3: 465-475. Doi: 10.3934/jmd.2007.1.465

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Quasi-states and the Poisson bracket on surfaces

Frol Zapolsky^1,

1.
School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978

Received: January 31, 2007

Revised: February 28, 2007

Published: March 2007

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Abstract

We present a convexity-type result concerning simple quasi-states on closed manifolds. As a corollary, an inequality emerges which relates the Poisson bracket to the measure of non-additivity of a simple quasi-state on a closed surface equipped with an area form. In addition, we prove that the uniform norm of the Poisson bracket of two functions on a surface is stable from below under $C^0$-perturbations.

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Mathematics Subject Classification: Primary: 53D99 Secondary: 28C15.

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