Skip to main content

Factors of type III

  • Conference paper
  • First Online:
K-Theory and Operator Algebras

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 575))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Anastasio and P.M. Willig, The Structure of Factors, Algonthnic Press, New York, 1974.

    Google Scholar 

  2. H. Araki, Structure of some von Neumann algebras with isolated discrete modular spectrum.

    Google Scholar 

  3. H. Araki and E.J. Woods, A classification of factors, Publications of Research Institute for Math. Sciences, Kyoto Univ., Ser. A 4 (1968), 51–130.

    Article  MathSciNet  MATH  Google Scholar 

  4. H. Choda, On the crossed product of abelian von Neumann algebras, II. Proc. Japan Acad. 43 (1967), 198–201.

    Article  Google Scholar 

  5. F. Combes, Poids sur une C*-algebra, J. Math. pures et oppl. 47 (1968), 57–100.

    MathSciNet  MATH  Google Scholar 

  6. _____, Poids associe une algebre hilbertinne a gauche, Compotio Math. 23 (1971), 49–77.

    MathSciNet  MATH  Google Scholar 

  7. A. Connes, Un nouvel invariant pour les algebres de von Neumann, C.R. Acad. Paris, Ser. A 273 (1971), 900–903; Calcul des deux invariants d'Araki et Woods par la theorie de Tomita et Takesaki, C.R. Acad. Paris, Ser. A 274 (1972), 175–177.

    MathSciNet  MATH  Google Scholar 

  8. _____, Une classification de facteurs de type III, Ann. Sci. Ecole Norm. Sup. 4 eme Ser. 6 (1973), 133–252.

    MathSciNet  MATH  Google Scholar 

  9. _____, Periodic automorphisms of the hyperfinite factor of type II1, preprint.

    Google Scholar 

  10. _____, Automorphism groups of II1-factors, Talk given at the International Conference on C*-algebras and Applications to physics held in Rome, March, 1975.

    Google Scholar 

  11. _____ and A. Van Daele, The group property of the invariant S(M), Math. Scand.

    Google Scholar 

  12. _____, and M. Takesaki, Flots des poids sur les facteurs de type III, C. R. Acad., Paris, Ser. A 278 (1974), 945–948.

    MathSciNet  MATH  Google Scholar 

  13. A. Connes and M. Takesaki, The flow of weights on factors of type III, to appear.

    Google Scholar 

  14. A. Van Daele, A new approach to the Tomita-Takesaki theory of generalized Hilbert algebras, J. Functional Analysis 15 (1974), 378–393.

    Article  MathSciNet  MATH  Google Scholar 

  15. H.A. Dye, On groups of measure preserving transformation, I, American J. Math. 81 (1959), 119–159; II, American J. Math. 85 (1963), 551–576.

    Article  MathSciNet  MATH  Google Scholar 

  16. R. Haag, N.M. Hugenholtz and M. Winnik, On the equilibrium states in quantum statistical mechanics, Comm. Math. Phys. 5 (1967), 215–236.

    Article  MathSciNet  MATH  Google Scholar 

  17. W. Krieger, An ergodic flows and the isomorphism of factors, to appear.

    Google Scholar 

  18. G.W. Mackey, Ergodic theory and virtual groups, Math. Ann. 166 (1966), 187–207.

    Article  MathSciNet  MATH  Google Scholar 

  19. D. McDuff, A countable infinity of II1-factors, Ann. Math. 90 (1969), 361–371.

    Article  MathSciNet  MATH  Google Scholar 

  20. _____, Uncountable many II1-factors, Ann. Math. 90 (1969), 372–377.

    Article  MathSciNet  MATH  Google Scholar 

  21. G.K. Pedersen, Measure theory for C*-algebras, Math. Scand. 19 (1966), 131–145.

    MathSciNet  Google Scholar 

  22. G.K. Pedersen and M. Takesaki, The Radon-Nikodym theorem for von Neumann algebras, Acta Math. 130 (1973), 53–87.

    Article  MathSciNet  MATH  Google Scholar 

  23. R.T. Powers, Representations of uniformly hyperfinite algebras and their associated von Neumann rings, Ann. Math. 86 (1967), 138–171.

    Article  MathSciNet  MATH  Google Scholar 

  24. S. Sakai, An uncountable number of II1 and II∞ factors, J. Functional Analysis 5 (1970), 236–246.

    Article  MathSciNet  MATH  Google Scholar 

  25. I.M. Singer, Automorphisms of finite factors, American J. Math. 77 (1955), 117–133.

    Article  MATH  Google Scholar 

  26. M. Takesaki, Tomita's theory of modular Hilbert algebras, Lecture Notes in Math., Springer-Verlag 128 (1970).

    Google Scholar 

  27. _____, Periodic and homogeneous states on a von Neumann algebras, I, Bull. Amer. Math. Soc. 79 (1973), 202–206; II, Bull. Amer. Math. Soc. 79 (1973), 416–420; III, Bull. Amer. Math. Soc. 79 (1973), 559–563.

    Article  MathSciNet  MATH  Google Scholar 

  28. _____, The structure of a von Neumann algebra with a homogeneous periodic state, Acta Math. 131 (1973), 79–121.

    Article  MathSciNet  MATH  Google Scholar 

  29. _____, Duality for crossed products and the structure of von Neumann algebras of type III, Acta Math. 131 (1973), 249–310.

    Article  MathSciNet  MATH  Google Scholar 

  30. M. Tomita, Standard forms of von Neumann algebras, the Vth Functional Analysis Symposium of the Math. Soc. of Japan, Sendai, (1967).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1977 Springer-Verlag Berlin · Heidelberg

About this paper

Cite this paper

Takesaki, M. (1977). Factors of type III. In: Morrel, B.B., Singer, I.M. (eds) K-Theory and Operator Algebras. Lecture Notes in Mathematics, vol 575. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0095708

Download citation

  • DOI: https://doi.org/10.1007/BFb0095708

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08133-3

  • Online ISBN: 978-3-540-37423-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics