Entropy in operator algebras
Recent advances in operator algebras - Orléans, 1992, Astérisque, no. 232 (1995), pp. 211-230.
@incollection{AST_1995__232__211_0,
     author = {St{\o}rmer, Erling},
     title = {Entropy in operator algebras},
     booktitle = {Recent advances in operator algebras - Orl\'eans, 1992},
     series = {Ast\'erisque},
     pages = {211--230},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {232},
     year = {1995},
     zbl = {0844.46033},
     language = {en},
     url = {http://archive.numdam.org/item/AST_1995__232__211_0/}
}
TY  - CHAP
AU  - Størmer, Erling
TI  - Entropy in operator algebras
BT  - Recent advances in operator algebras - Orléans, 1992
AU  - Collectif
T3  - Astérisque
PY  - 1995
SP  - 211
EP  - 230
IS  - 232
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_1995__232__211_0/
LA  - en
ID  - AST_1995__232__211_0
ER  - 
%0 Book Section
%A Størmer, Erling
%T Entropy in operator algebras
%B Recent advances in operator algebras - Orléans, 1992
%A Collectif
%S Astérisque
%D 1995
%P 211-230
%N 232
%I Société mathématique de France
%U http://archive.numdam.org/item/AST_1995__232__211_0/
%G en
%F AST_1995__232__211_0
Størmer, Erling. Entropy in operator algebras, dans Recent advances in operator algebras - Orléans, 1992, Astérisque, no. 232 (1995), pp. 211-230. http://archive.numdam.org/item/AST_1995__232__211_0/

[1] Araki, H., Relative entropy of states of von Neumann algebras I, II, Publ. RIMS, Kyoto Univ. 11 (1976), 809-833 | DOI | MR | Zbl

Araki, H., Relative entropy of states of von Neumann algebras I, II, Publ. RIMS, Kyoto Univ. 13 (1977), 173-192. | DOI | MR | Zbl

[2] Besson, O., On the entropy in II 1 von Neumann algebras, Ergod. Th. & Dynam. Sys. 1 (1981), 419-429. | DOI | MR | Zbl

[3] Besson, O., On the entropy of quantum Markov states, Lecture Notes in Math. 1136, pp. 81-89. Springer-Verlag 1985. | MR | Zbl

[4] Choda, M., Entropy for *-endomorphisms and relative entropy for subalgebras, J. Operator Theory, 25 (1991), 125-140. | MR | Zbl

[5] Connes, A., Entropie de Kolmogoroff Sinai et mechanique statistique quantique, C. R. Acad. Sci. Paris 301 (1985), 1-6. | MR | Zbl

[6] Connes, A., Feldman, J., and Weiss, B., An amenable equivalence relation is generated by a single transformation, Ergod. Th. & Dynam. Sys. 1 (1981), 431-450. | DOI | MR | Zbl

[7] Connes, A., Narnhofer, H., and Thirring W., Dynamical entropy of C * -algebras and von Neumann algebras, Commun. Math. Phys. 112 (1987), 691-719. | DOI | MR | Zbl

[8] Connes, A., and Størmer, E., Entropy of automorphisms of II 1 von Neumann algebras, Acta math. 134 (1975), 289-306. | DOI | MR | Zbl

[9] Connes, A., and Størmer, E., A connection between the classical and the quantum mechanical entropies, Operator Algebras and Group Representations, Monographs and Studies in Math. 17. Pitman 1984, 113-123. | MR | Zbl

[10] Evans, D. E., Entropy of automorphisms of AF-algebras, Publ. RIMS Kyoto Univ. 18 (1982), 1045-1051. | DOI | MR | Zbl

[11] Fannes, M., The entropy density of quasi free states, Commun. Math. Phys. 31 (1973), 279-290. | DOI | MR | Zbl

[12] Gaure, S., Free shifts of factors, Thesis, Univ. of Oslo, To appear. | Zbl

[13] Hudetz, T., Quantenmechanische topologische Entropie, Thesis, Univ. Wien, 1992.

[14] Jones, V. F. R., Index for subfactors, Invent. Math. 72 (1983), 1-25. | DOI | EuDML | MR | Zbl

[15] Kosaki, H., Relative entropy of states: a variational expression, J. Operator Theory 16 (1986), 335-348. | MR | Zbl

[16] Lieb, E. H., Convex trace functions and the Wigner-Yanase-Dyson conjecture, Advances in Math. 11 (1973), 267-288. | DOI | MR | Zbl

[17] Lieb, E. H., and Ruskai, M. B., Proof of the strong subadditivity of quantum mechanical entropy, J. Math. Phys. 14 (1973), 1938-1941. | DOI | MR

[18] Narnhofer, N., and Thirring, W., Dynamical entropy of quasifree automorphisms, Letters Math. Phys. 14 (1987), 89-96. | DOI | MR | Zbl

[19] Narnhofer, H., and Thirring, W., Dynamical entropy of quantum systems and their Abelian counterpart, To appear. | DOI | MR | Zbl

[20] Park, Y. M., and Shin, H. H., Dynamical entropy of quasi-local algebras in quantum statistical mechanics, Commun. Math., Phys. | MR | Zbl

[21] Park, Y. M., and Shin, H. H., Dynamical entropy of space translations of CAR and CCR algebras with respect to quasi-free states, To appear. | MR | Zbl

[22] Pimsner, M., and Popa, S., Entropy and index for subfactors, Ann. Sci. École Norm. Sup. Ser. 4, 19 (1986), 57-106. | DOI | EuDML | Numdam | MR | Zbl

[23] Popa, S., Maximal injective subalgebras in type II 1 factors, Advances in Math. 50 (1983), 27-48. | DOI | MR | Zbl

[24] Popa, S., Notes on Cartan subalgebras in type II 1 factors, Math. Scand. 57 (1985), 171-188. | DOI | EuDML | MR | Zbl

[25] Pusz, W., and Woronowicz, S., Form convex functions and the WYDL and other inequalities, Letters Math. Phys. 2 (1978), 505-512. | DOI | MR | Zbl

[26] Quasthoff, U., Shift automorphisms of the hyperfinite factor, Math. Nachtrichten 131 (1987), 101-106. | DOI | MR | Zbl

[27] Quasthoff, U., Continuous outer actions of the hyperfinite factor, Proc. conf. on ergodic th. II, Georgenthal 1986, pp. 166-170, Teuler-Texte Math. 94, Teulner, Leipzig 1987. | MR | Zbl

[28] Sauvageot, J-L., and Thouvenot, J-P., Une nouvelle définition de l'entropie dynamique des systèmes non commutatifs, To appear. | DOI | MR | Zbl

[29] Størmer, E., Entropy of some automorphisms of the II 1 -factor of the free group in infinite number of generators, Invent. Math. 110 (1992), 63-73. | DOI | EuDML | MR | Zbl

[30] Strømer, E., Entropy of some inner automorphisms of the hyperfinite II 1 -factor, International J. Math., To appear. | Zbl

[31] Størmer, E., and Voiculescu, D., Entropy of Bogoliubov automorphisms of the canonical anticommutation relations, Commun. Math. Phys. 133 (1990), 521- 542. | DOI | MR | Zbl

[32] Voiculescu, D., Entropy of dynamical systems and perturbations of operators, Ergod. Th. & Dynam. Sys. 11 (1991), 779-786. | DOI | MR | Zbl

[33] Voiculescu, D., Entropy of dynamical systems and perturbations of operators, II. To appear. | MR | Zbl

[34] Walters, P., An introduction to ergodic theory, Graduate Texts in Math. 79, Springer-Verlag. | MR | Zbl