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On the entropy in II1 von Neumann algebras

Published online by Cambridge University Press:  19 September 2008

O. Besson
O. Besson
Affiliation:
Département de Mathématiques, Ecole Polytechnique Fédérale, Lausanne, Switzerland
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Abstract

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Let α be an automorphism of a finite von Neumann algebra and let H(α) be its Connes-Størmer's entropy. We show that H(α) = 0 if α is the induced automorphism on the crossed product of a Lebesgue space by a pure point spectrum transformation. We also show that H is not continuous in α and we compute H(α) for some α.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 4 , December 1981 , pp. 419 - 429
Copyright
Copyright © Cambridge University Press 1981

References

REFERENCES

[1]Aubert, P. L.. Théorie de Galois pour une W*-algèbre. Comment. Math. Helvet. 51 (1976), 411–433.Google Scholar
[2]Connes, A.. A factor non anti-isomorphic to itself. Ann. of Math. 101 (1975), 536–554.Google Scholar
[3]Connes, A.. Outer conjugacy classes of automorphisms of factors. Ann. Sc. Ec. Norm. Sup. 8 (1975), 383–420.Google Scholar
[4]Connes, A. & Størmer, E.. Entropy for automorphisms of II1 von Neumann algebras. Acta Math. 134 (1975), 289–306.Google Scholar
[5]Connes, A. & Størmer, E.. A connection between the classical and the quantum mechanical entropies. Preprint.Google Scholar
[6]David, M. C.. Sur quelques problèmes de théorie ergodique non commutative. Publ. Math. Univ. P. & M. Curie. Preprint no. 19 (1978).Google Scholar
[7]Haagerup, U.. The standard form of von Neumann algebras. Math. Scan. 37 (1975), 271–283.Google Scholar
[8]Sinai, Ya. G.. Introduction to Ergodic Theory. Princeton University Press: New Jersey, 1976.Google Scholar
[9]Takesaki, M.. Duality for crossed products and the structure of von Neumann algebras of type III. Acta Math. 131 (1973), 249–310.Google Scholar
[10]Umegaki, H.. Conditional expectation in an operator algebra IV (Entropy and information). Kodai Mat. Sem. Rep. 14 (1962), 59–85.Google Scholar
[11]Walters, P.. Ergodic Theory. Springer Lecture Notes in Math. 458 (1975).Google Scholar