Tohoku Mathematical Journal

The flow of weights on factors of type ${\rm III}$

Alain Connes and Masamichi Takesaki

Full-text: Open access

Article information

Source
Tohoku Math. J. (2) Volume 29, Number 4 (1977), 473-575.

Dates
First available in Project Euclid: 4 May 2007

Permanent link to this document
http://projecteuclid.org/euclid.tmj/1178240493

Digital Object Identifier
doi:10.2748/tmj/1178240493

Mathematical Reviews number (MathSciNet)
MR0480760

Zentralblatt MATH identifier
0408.46047

Subjects
Primary: 46L10: General theory of von Neumann algebras
Secondary: 46L35: Classifications of $C^*$-algebras 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]

Citation

Connes, Alain; Takesaki, Masamichi. The flow of weights on factors of type ${\rm III}$. Tohoku Math. J. (2) 29 (1977), no. 4, 473--575. doi:10.2748/tmj/1178240493. http://projecteuclid.org/euclid.tmj/1178240493.


Export citation

References

  • [1] C. AKEMANN, The dual space of an operator algebra, Trans. Amer. Math. Soc., 126 (1967), pp. 286-302.
  • [2] N. BOURBAKI, Topologic Generate, Chapter 9, 2nd. Ed., Paris (1958)
  • [3] A. CONNES, Une classification des facteurs de type III, Ann. Sci. Ecole Norm. Sup., erne Ser., 6 (1973), pp. 133-252.
  • [4] A. CONNES, tats presque periodiques sur une algebra de von Neumann, C. R. Acad. Sci., Paris, Ser. A 274 (1972), pp. 1402-1405.
  • [5] A. CONNES, Caracterisation des algebres de von Neumann comme espaces vectoriels or donnes, to appear.
  • [6] A. CONNES, Sur le theoreme de Radon-Nikodym pour les normaux fideles semi-finis, t appear.
  • [7] A. CONNES AND M. TAKESAKI, Flots des poids sur les facteurs de type III, C. R. Acad Sci., Paris, Ser. A 278 (1974), pp. 945-948.
  • [8] T. DIGERNESS, Poids dual sur un produit croise, C. R. Sci., Paris, Ser. A 278 (1974), pp 937-940.
  • [9] T. DIGERNESS, Duality for weights on covariant systems and its applications, Thesis, UCLA (1975).
  • [10] R. GODEMENT, Theorie des faisceaux, Herman, Paris, (1964)
  • [11] R. KADISON AND J. RINGROSE, Derivations and automorphisms of operator algebras, Comm. Math. Phys., 4 (1967), pp. 32-63.
  • [12] U. KRENGEL, Darstellungssatze fur Strmungen und Halb-strmungen II, Math. Ann 182 (1969), pp. 1-39.
  • [13] W. KRIEGER, On ergodic flows and the isomorphism of factors, to appear
  • [14] I. KUBO, Quasi-flows, Nagoya Math. J., 35 (1669), 1-30
  • [15] M. LANDSTAD, Duality theory of covariant systems, to appear
  • [16] G. MACKEY, Ergodic theory and virtual groups, Math. Ann., 166 (1966), pp. 187-207
  • [17] G. MACKEY, Borel structures in groups and their duals, Trans. Amer. Math. Soc., 8 (1957), pp. 265-311.
  • [18] C. C. MOORE, Group extensions and group cohomology, Group representations in Mathe matics and physics, Lecture Notes in Physics, Springer, 6 (1970), pp. 17-35.
  • [19] F. J. MURRAY AND V. VONNEUMANN, On rings of operators, Ann. of Math., 37 (1936), pp. 116-229.
  • [20] F. J. MURRAY AND J. VONNEUMANN, On rings of operators IV, Ann. of Math., 44 (1943), pp. 716-808.
  • [21] M. NAKAMURA AND Z. TAKEDA, On some elementary properties of the crossed product of von Neumann algebras, Proc. Japan Acad., 34 (1958), pp. 489-494.
  • [22] M. NAKAMURA AND Z. TAKADA, A Galois theory for finite factors, Proc. Japan Acad., 3 (1960), 258-260.
  • [23] M. NAKAMURA AND Z. TAKADA, On the fundamental theorem of the Galois theory fo finite factors, Proc. Japan Acad., 36 (1960), pp. 313-318.
  • [24] G. K. PEDERSON AND M. TAKESAKI, The Radon-Nikodym theorem for von Neuman algebras, Acta Math., 130 (1973), pp. 53-87.
  • [25] W. RUDIN, Fourier analysis on groups, Intersciences, (1960)
  • [26] J. L. SAUVAGEOT, Sur le type du produit croise d'une algebre de von Neumann par u groupe loealement compact d'automorphisms, C. R. Acad. Sci. Paris, Ser. A, 278, (1974), pp. 941-944.
  • [27] N. SUZUKI, Cross products of rings of operators, Thoku Math. J., 11 (1959), pp. 113-124
  • [28] M. TAKESAKI, A generalized commutation relation for the regular representation, Bull Soc. Math., France, 97 (1969), pp. 289-297.
  • [29] M. TAKESAKI, Tomita's theory of modular Hubert algebras and its applications, Lectur Notes in Math., 128, Springer, (1970).
  • [30] M. TAKESAKI, Duality for crossed products and the structure of von Neumann algebra of type III, Acta Math., 131 (1974), pp. 249-310.
  • [31] M. TAKESAKI AND N. TATSUUMA, Duality and subgroups, Ann. of Math., 93 (1971), pp 344-364.
  • [32] G. ZELLER-MEIER, Produits croises d'une C*-algebra par un groupe d'automorphismes, J. Math. Pures Appl., 47 (1968), pp. 101-239.