Inventiones mathematicae

, Volume 123, Issue 3, pp 453–466 | Cite as

On tensor products of von Neumann algebras

  • L. Ge
  • R. Kadison


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [C]
    A. Connes: Classification of injective factors. Ann. Math. 104, 73–115 (1976)CrossRefMathSciNetGoogle Scholar
  2. [E-L]
    E. Effros, E.C. Lance: Tensor products of Operator algebras. Adv. Math. 25, 1–34 (1977)MATHCrossRefMathSciNetGoogle Scholar
  3. [F-K]
    B. Fuglede, R. Kadison: On a conjecture of Murray and von Neumann. Proc. Nat. Acad. Sci. (USA) 37, 420–425 (1951)MATHCrossRefMathSciNetGoogle Scholar
  4. [Ge]
    L. Ge: On maximal injective subalgebras of factors. Adv. Math, (to appear)Google Scholar
  5. [Gl]
    J. Glimm: On a certain class of Operator algebras. Trans. Amer. Math. Soc. 95, 318–340 (1960)MATHCrossRefMathSciNetGoogle Scholar
  6. [Gr]
    A. Grothendieck: Produits tensoriels topologique et espaces nucleaires. Memoirs Amer. Math. Soc. 16, (1955)Google Scholar
  7. [H]
    H. Halpern: Essential central spectrum and range for elements of a von Neumann algebra. Pacific J. Math. 43, 349–380 (1972)MATHMathSciNetGoogle Scholar
  8. [Haa]
    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)MATHCrossRefMathSciNetGoogle Scholar
  9. [H-Z]
    U. Haagerup, L. Zsido: Sur la propriete Dixmier pour les C*-algébres. C.R. Acad. Sci. Paris 298 Série I, 173–176 (1984)MATHMathSciNetGoogle Scholar
  10. [K1]
    R. Kadison: Unitary invariants for representations of Operator algebras. Ann. Math. 66, 304–379 (1957)CrossRefMathSciNetGoogle Scholar
  11. [K2]
    R. Kadison: The trace in finite Operator algebras. Proc. Amer. Math. Soc. 12, 973–977 (1961)MATHCrossRefMathSciNetGoogle Scholar
  12. [K3]
    R. Kadison: Transformations of states in Operator theory and dynamics. Topology, 3, 177–198 (1965)CrossRefMathSciNetGoogle Scholar
  13. [K-R]
    R. Kadison, J. Ringrose: Derivations and automorphisms of Operator algebras. Commun. Math. Phys., 4, 32–63 (1967)MATHCrossRefMathSciNetGoogle Scholar
  14. [K-R I-IV]
    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 1992MATHGoogle Scholar
  15. [Kr]
    J. Kraus: The slice map problem for σ-weakly closed subspaces of von Neumann algebras. Trans. Am. Math. Soc. 279, 357–376 (1983)MATHCrossRefMathSciNetGoogle Scholar
  16. [M-vN]
    F. Murray, J. von Neumann: On rings of Operators. Ann. Math. 37, 116–229 (1936)CrossRefGoogle Scholar
  17. [vN]
    J. von Neumann: Zur Algebra der Funktionaloperationen und Theorie der normalen Operatoren. Math. Ann. 102, 370–427 (1930)CrossRefMathSciNetGoogle Scholar
  18. [P1]
    S. Popa: Maximal injective subalgebras in factors associated with free groups. Adv. Math. 50, 27–48 (1983)MATHCrossRefGoogle Scholar
  19. [P2]
    S. Popa: A short proof of “injectivity implies hyperfiniteness” for finite von Neumann algebras. J. Operator Theory 16, 261–272 (1986)MATHMathSciNetGoogle Scholar
  20. [R-vD]
    M. Rieffei, A. van Daele: The commutation theorem for tensor products of von Neumann algebras. Bull. London Math. Soc. 7, 257–260 (1975)CrossRefMathSciNetGoogle Scholar
  21. [R]
    J. Ringrose: On the Dixmier approximation theorem. Proc. London Math. Soc. 49, 37–57 (1984)MATHCrossRefMathSciNetGoogle Scholar
  22. [S]
    S. Sakai: A characterization of W*-algebras. Pacific J. Math. 6, 763–773 (1956)MATHMathSciNetGoogle Scholar
  23. [Ta1]
    M. Takesaki: On the cross-norm of the direct product of C*-algebras. Tôhoku Math. J. 16, 111–122 (1964)CrossRefMathSciNetGoogle Scholar
  24. [Ta2]
    M. Takesaki: Tomita’s Theory of Modular Hubert Algebras and Its Applications. Lecture Notes in Math. Vol. 128. Springer-Verlag, Heidelberg, 1970Google Scholar
  25. [Ta3]
    M. Takesaki: A short proof for the commutation theorem Open image in new window. Lectures on Operator Algebras. Lecture Notes in Math. Vol. 247, 780–786. Springer-Verlag, Heidelberg, 1972Google Scholar
  26. [T]
    M. Tomita: Standard forms of von Neumann algebras. Preprint 1967, Fifth Functional Analysis Symposium of the Math. Soc. of JapanGoogle Scholar
  27. [To1]
    J. Tomiyama: On the projections of norm one in W*-algebras. Proc. Japan Acad. 33, 608–612 (1957)MATHCrossRefMathSciNetGoogle Scholar
  28. [To2]
    J. Tomiyama: Tensor products and projections of norm one in von Neumann algebras. Seminar notes of the Math. Institute, University of Copenhagen (1970)Google Scholar
  29. [W]
    S. Wassermann: The slice map problem for C*-algebras. Proc. London Math. Soc. 32, 537–559 (1976)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • L. Ge
    • 1
  • R. Kadison
    • 2
  1. 1.Department of MathematicsMITCambridgeUSA
  2. 2.Department of MathematicsUniversity of PennsylvaniaPhiladelphiaUSA

Personalised recommendations