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The eigenvectors of semigroups of positive maps on von Neumann algebras

Published online by Cambridge University Press:  13 October 2009

ANDRZEJ ŁUCZAK
ANDRZEJ ŁUCZAK*
Affiliation:
Faculty of Mathematics and Computer Science, Łódź University, ul. S. Banacha 22, 90-238 Łódź, Poland (email: [email protected])
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Abstract

The eigenvectors of an ergodic semigroup of linear normal positive unital maps on a von Neumann algebra are described. Moreover, it is shown by means of examples that mere positivity of the maps in question is not sufficient for Frobenius theory as in Albeverio and Høegh-Krohn [Frobenius theory of positive maps of von Neumann algebras. Comm. Math. Phys.64 (1978), 83–94] to hold.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 5 , October 2010 , pp. 1495 - 1502
Copyright
Copyright © Cambridge University Press 2009

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References

[1]Albeverio, S. and Høegh-Krohn, R.. Frobenius theory of positive maps of von Neumann algebras. Comm. Math. Phys. 64 (1978), 83–94.CrossRefGoogle Scholar
[2]Groh, U.. Positive semigroups on C *- and W *-algebras. One-parameter Semigroups of Positive Operators (Lecture Notes in Mathematics, 1184). Ed. Nagel, R.. Springer, Berlin, 1986, pp. 369–425.CrossRefGoogle Scholar
[3]Łuczak, A.. Eigenvalues and eigenspaces of quantum dynamical systems and their tensor products. J. Math. Anal. Appl. 221 (1998), 13–32.CrossRefGoogle Scholar
[4]Takesaki, M.. Theory of Operator Algebras. Springer, Berlin, 1979.CrossRefGoogle Scholar
[5]Watanabe, S.. Asymptotic behavior and eigenvalues of dynamical semi-groups on operator algebras. J. Math. Anal. Appl. 86 (1982), 411–424.CrossRefGoogle Scholar