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Entropy for automorphisms of \(II_1\) von Neumann algebras. (English) Zbl 0326.46032

MSC:
46L10 General theory of von Neumann algebras
28D05 Measure-preserving transformations
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[1] Behncke, H., Topics inC *–and von Neumann algebras.Lectures in operator algebras, Lecture Notes Math. 247, Springer-Verlag, Berlin-Heidelberg-New York 1972. 2–55.
[2] Choi, M. D., Positive linear maps onC *-algebras,Canad. J. Math., 24 (1972), 520–529. · Zbl 0235.46090
[3] Dixmier, J.,Les algébres d’opérateurs dans l’espace hilbertien. Paris, Gauthier-Villars 1969.
[4] Kovács, I. &Szücs, J., Egodic type theorems in von Neumann algebras.Acta Sci. Math., 27 (1966), 233–246. · Zbl 0143.36105
[5] Lieb, E. H., Convex trace functions and the Wigner-Yanase-Dyson conjecture.Advances Math., 11 (1973), 267–288. · Zbl 0267.46055
[6] Lieb, E. H. &Ruskai, M. B., Proof of the strong subadditivity of quantum mechanical entropy.J. Math. Physics, 14 (1973), 1938–1941.
[7] Lindblad, G., Entropy, information and quantum measurements.Commun. Math. Phys., 33 (1973), 305–322.
[8] –, Expectations and entropy inequalities for finite quantum systems.Commun. Math. Phys., 39 (1974), 111–119. · Zbl 0294.46052
[9] Nakamura, M. &Umegaki, H., A note on the entropy for operator algebras.Proc. Japan Acad., 37 (1961), 149–154. · Zbl 0101.09401
[10] Powers, R. T., Representations of uniformly hyperfinite algebras and their associated von Neumann rings.Ann. of Math., 86 (1967), 138–171. · Zbl 0157.20605
[11] Ruelle, D.,Statistical mechanics, rigorous results. W.A. Benjamin, New York, Amsterdam 1969. · Zbl 0177.57301
[12] Sakai, S. C * and W * algebras. Ergebnisse der Math., Band 60.
[13] Størmer, E., Symmetric states of infinite tensor products ofC *-algebras.J. Funct. Anal., 3 (1969), 48–68. · Zbl 0167.43403
[14] –, Asymptotically abelian system.Cargese lectures in physics, Vol. 4, 195–213, New York, Gordon and Breach 1970.
[15] Takesaki, M.,Tomita’s theory of modular Hilbert algebras and its applications. Lecture Notes Math. 128, Berlin-Heidelberg-New York, Springer 1970. · Zbl 0193.42502
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