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C*-dynamical systems for which the tensor product formula for entropy fails

Published online by Cambridge University Press:  14 October 2010

Heide Narnhofer ,
Walter Thirring  and
Erling Størmer
Heide Narnhofer
Affiliation:
Institut für Theoretische Physik, Universität Wien, A-1090 Wien, Austria, and International Erwin Schrödinger Institute for Mathematical Physics, A-1090 Wien, Pasteurgasse 6, Austria
Walter Thirring
Affiliation:
Institut für Theoretische Physik, Universität Wien, A-1090 Wien, Austria, and International Erwin Schrödinger Institute for Mathematical Physics, A-1090 Wien, Pasteurgasse 6, Austria
Erling Størmer
Affiliation:
Department of Mathematics, University of Oslo, P.b. 1053, Blindern, N-0316 Oslo, Norway†
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Abstract

It is shown that for a class of simple AF-algebras generated by a sequence of self-adjoint unitaries (sn) the entropy of the shift α(sn) = sn+1 with respect to the unique invariant trace υ satisfies hϕøϕ (α⊗α) = log2, while hφ(α) = 0.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 5 , October 1995 , pp. 961 - 968
Copyright
Copyright © Cambridge University Press 1995

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References

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