Skip to main content
SpringerLink
Log in

On tensor products of von Neumann algebras

  • Published:
Inventiones mathematicae Aims and scope

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. A. Connes: Classification of injective factors. Ann. Math. 104, 73–115 (1976)

    Article  MathSciNet  Google Scholar 

  2. E. Effros, E.C. Lance: Tensor products of Operator algebras. Adv. Math. 25, 1–34 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  3. B. Fuglede, R. Kadison: On a conjecture of Murray and von Neumann. Proc. Nat. Acad. Sci. (USA) 37, 420–425 (1951)

    Article  MATH  MathSciNet  Google Scholar 

  4. L. Ge: On maximal injective subalgebras of factors. Adv. Math, (to appear)

  5. J. Glimm: On a certain class of Operator algebras. Trans. Amer. Math. Soc. 95, 318–340 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Grothendieck: Produits tensoriels topologique et espaces nucleaires. Memoirs Amer. Math. Soc. 16, (1955)

  7. H. Halpern: Essential central spectrum and range for elements of a von Neumann algebra. Pacific J. Math. 43, 349–380 (1972)

    MATH  MathSciNet  Google Scholar 

  8. U. Haagerup: A new proof of the equivalence of injeetivity and hyperfiniteness for factors on a separable Hilbert space. J. Fnal. Anal. 62, 160–201 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  9. U. Haagerup, L. Zsido: Sur la propriete Dixmier pour les C*-algébres. C.R. Acad. Sci. Paris 298 Série I, 173–176 (1984)

    MATH  MathSciNet  Google Scholar 

  10. R. Kadison: Unitary invariants for representations of Operator algebras. Ann. Math. 66, 304–379 (1957)

    Article  MathSciNet  Google Scholar 

  11. R. Kadison: The trace in finite Operator algebras. Proc. Amer. Math. Soc. 12, 973–977 (1961)

    Article  MATH  MathSciNet  Google Scholar 

  12. R. Kadison: Transformations of states in Operator theory and dynamics. Topology, 3, 177–198 (1965)

    Article  MathSciNet  Google Scholar 

  13. R. Kadison, J. Ringrose: Derivations and automorphisms of Operator algebras. Commun. Math. Phys., 4, 32–63 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  14. R. Kadison, J. Ringrose: Fundamentals of the Theory of Operator Algebras. Academic Press, Orlando, Vol. I, 1983, Vol. II, 1986, Birkhäuser, Boston, Vol. III, 1991, Vol.IV 1992

    MATH  Google Scholar 

  15. J. Kraus: The slice map problem for σ-weakly closed subspaces of von Neumann algebras. Trans. Am. Math. Soc. 279, 357–376 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  16. F. Murray, J. von Neumann: On rings of Operators. Ann. Math. 37, 116–229 (1936)

    Article  Google Scholar 

  17. J. von Neumann: Zur Algebra der Funktionaloperationen und Theorie der normalen Operatoren. Math. Ann. 102, 370–427 (1930)

    Article  MathSciNet  Google Scholar 

  18. S. Popa: Maximal injective subalgebras in factors associated with free groups. Adv. Math. 50, 27–48 (1983)

    Article  MATH  Google Scholar 

  19. S. Popa: A short proof of “injectivity implies hyperfiniteness” for finite von Neumann algebras. J. Operator Theory 16, 261–272 (1986)

    MATH  MathSciNet  Google Scholar 

  20. M. Rieffei, A. van Daele: The commutation theorem for tensor products of von Neumann algebras. Bull. London Math. Soc. 7, 257–260 (1975)

    Article  MathSciNet  Google Scholar 

  21. J. Ringrose: On the Dixmier approximation theorem. Proc. London Math. Soc. 49, 37–57 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  22. S. Sakai: A characterization of W*-algebras. Pacific J. Math. 6, 763–773 (1956)

    MATH  MathSciNet  Google Scholar 

  23. M. Takesaki: On the cross-norm of the direct product of C*-algebras. Tôhoku Math. J. 16, 111–122 (1964)

    Article  MathSciNet  Google Scholar 

  24. M. Takesaki: Tomita’s Theory of Modular Hubert Algebras and Its Applications. Lecture Notes in Math. Vol. 128. Springer-Verlag, Heidelberg, 1970

    Google Scholar 

  25. M. Takesaki: A short proof for the commutation theorem . Lectures on Operator Algebras. Lecture Notes in Math. Vol. 247, 780–786. Springer-Verlag, Heidelberg, 1972

    Google Scholar 

  26. M. Tomita: Standard forms of von Neumann algebras. Preprint 1967, Fifth Functional Analysis Symposium of the Math. Soc. of Japan

  27. J. Tomiyama: On the projections of norm one in W*-algebras. Proc. Japan Acad. 33, 608–612 (1957)

    Article  MATH  MathSciNet  Google Scholar 

  28. J. Tomiyama: Tensor products and projections of norm one in von Neumann algebras. Seminar notes of the Math. Institute, University of Copenhagen (1970)

  29. S. Wassermann: The slice map problem for C*-algebras. Proc. London Math. Soc. 32, 537–559 (1976)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, MIT, 02139-4307, Cambridge, MA, USA

    L. Ge

  2. Department of Mathematics, University of Pennsylvania, 19104-6395, Philadelphia, PA, USA

    R. Kadison

Authors
  1. L. Ge
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Kadison
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Masamichi Takesaki for his many fundamental contributions to Non-commutative Analysis of the occasion of his sixtieth birthday

Oblatum 18-X-1995

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ge, L., Kadison, R. On tensor products of von Neumann algebras. Invent. math. 123, 453–466 (1996). https://doi.org/10.1007/s002220050036

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s002220050036

Keywords

Search

Navigation