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http://dx.doi.org/10.4134/BKMS.2004.41.1.189

QUANTUM DYNAMICAL SEMIGROUP AND ITS ASYMPTOTIC BEHAVIORS  

Choi, Veni (Department of Mathematics, Yonsei University)
Publication Information
Bulletin of the Korean Mathematical Society / v.41, no.1, 2004 , pp. 189-198 More about this Journal
Abstract
In this study we consider quantum dynamical semi-group with a normal faithful invariant state. A quantum dynamical semigroup $\alpha\;=\;\{{\alpha}_t\}_{t{\geq}0}$ is a class of linear normal identity-preserving mappings on a von Neumann algebra M with semigroup property and some positivity condition. We investigate the asymptotic behaviors of the semigroup such as ergodicity or mixing properties in terms of their eigenvalues under the assumption that the semigroup satisfies positivity. This extends the result of [13] which is obtained under the assumption that the semi group satisfy 2-positivity.
Keywords
quantum dynamical semigroup; positivity; Schwarz inequality; Jordan product; ergodicity; weak mixing;
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