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Periodic and homogeneous states on a von Neumann algebra. I. (English) Zbl 0262.46064


MSC:

46L10 General theory of von Neumann algebras
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[1] Huzihiro Araki and E. J. Woods, A classification of factors, Publ. Res. Inst. Math. Sci. Ser. A 4 (1968/1969), 51 – 130. · Zbl 0206.12901
[2] Alain Connes, Un nouvel invariant pour les algèbres de von Neumann, C. R. Acad. Sci. Paris Sér. A-B 273 (1971), A900 – A903 (French). · Zbl 0227.46067
[3] Alain Connes, Calcul des deux invariants d’Araki et Woods par la théorie de Tomita et Takesaki, C. R. Acad. Sci. Paris Sér. A-B 274 (1972), A175 – A177 (French). · Zbl 0227.46068
[4] A. Connes, Groupe modulaire d’une algebre de von Neumann de genre denombrable (to appear). · Zbl 0245.46091
[5] Jacques Dixmier, Les algèbres d’opérateurs dans l’espace hilbertien (Algèbres de von Neumann), Cahiers scientifiques, Fascicule XXV, Gauthier-Villars, Paris, 1957 (French). · Zbl 0088.32304
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[8] Robert T. Powers, Representations of uniformly hyperfinite algebras and their associated von Neumann rings, Ann. of Math. (2) 86 (1967), 138 – 171. · Zbl 0157.20605 · doi:10.2307/1970364
[9] Erling Størmer, Spectra of states and asymptotically abelian \?*-algebras, Papers from the ”Open House for Functional Analysts” (Aarhus Univ., Aarhus, 1972) Mat. Inst., Aarhus Univ., Aarhus, 1972, pp. 7 pp. Various Publications Ser., No. 23. · Zbl 0245.46085
[10] M. Takesaki, Tomita’s theory of modular Hilbert algebras and its applications, Lecture Notes in Mathematics, Vol. 128, Springer-Verlag, Berlin-New York, 1970. · Zbl 0193.42502
[11] M. Takesaki, States and automorphisms of operator algebras. Standard representations and the Kubo-Martin-Schwinger boundary condition, Summer Rencontres in Mathematics and Physics, Battelle Seattle, 1971. · Zbl 0258.46055
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