The Commutation Theorem for Tensor Products over von Neumann Algebras

Journal of Functional Analysis

Volumn 165, Issue 2, 1999, Pages 293-346

  Stratila, Şerban ^a   Zsidó, László ^b  

^a INSTITUTE OF MATHEMATICS   (Romania)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

algebras; Commutants; Conditional expectations; Dixmier sets; Hilbert modules; Homogenous commutative W; Tensor products; Von Neumann algebras

Indexed keywords

EID: 0000669786     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1999.3408     Document Type: Article

References (36)

1. Aumann R. J. Measurable utility and the measurable choice theorem. La Decision. 2. Agregation et Dynamique des Ordres de Preference. 1969;Presses du CNRS, Paris. p. 15-26.
2. Castaing C., Valadier M. Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics. 580:1977;Springer-Verlag, New York/Berlin.
3. Connes A. Une classification des facteurs de type III. Ann. Sci. Ecole Norm. Sup. 6:1973;133-252.
4. Connes A. Classification of injective factors. Ann. of Math. 104:1976;73-115.
5. Connes A., Takesaki M. The flow of weights on a factor of type III. Tôhoku Math. J. 29:1977;473-575.
6. Conway J. B. The numerical range and a certain convex set in an infinite factor. J. Funct. Anal. 5:1970;428-435.
7. D'Antoni C., Longo R. Interpolation by type I factors and the flip automorphism. J. Funct. Anal. 51:1983;361-371.
8. J. Dixmier, Les Algébres d'Opérateurs dans l'Espace Hilbertien (Algébres de von Neumann), Gauthier-Villars, Paris, 1957, 1969.
9. Dixmier J. Les anneaux d'opérateurs de classe finie. Ann. Sci. Ecole Norm. Sup. 66:1949;209-261.
10. Fremlin D. H. Measure algebras. Monk J. D., Bonnet R. Handbook of Boolean Algebras. 1989;877-980 North-Holland, Amsterdam.
11. Ge L., Kadison R. V. On tensor products of von Neumann algebras. Invent. Math. 123:1996;453-466.
12. Goodearl K. R. Notes on Real and Complex C*-Algebras. 1982;Shiva Publ. Comp.
13. Halpern H. Module homomorphisms of a von Neumann algebra into its center. Trans. Amer. Math. Soc. 140:1969;183-193.
14. Halpern H. Irreducible Module homomorphisms of a von Neumann algebra into its center. Trans. Amer. Math. Soc. 140:1969;195-221.
15. Halpern H. Integral decompositions of functionals on C*-algebras. Trans. Amer. Math. Soc. 168:1972;371-385.
16. Halpern H. Essential central spectrum and range for elements of a von Neumann algebra. Pacific J. Math. 43:1972;349-380.
17. Kadison R. V. Strong continuity of operator functions. Pacific J. Math. 26:1968;121-129.
18. Kaplansky I. Modules over operator algebras. Amer. J. Math. 75:1953;839-858.
19. Maharam D. On homogeneous measure algebras. Proc. Nat. Acad. Sci. U.SA. 28:1942;108-111.
20. Paschke W. Inner product modules over B*-algebras. Trans. Amer. Math. Soc. 182:1973;443-468.
21. Popa S. Maximal injective subalgebras in factors associated with free groups. Adv. Math. 50:1983;27-48.
22. Rieffel M. A., Van Daele A. The commutation theorem for tensor products of von Neumann algebras. Bull. London Math. Soc. 7:1975;257-260.
23. Sakai S. C*-Algebras and W*-Algebras. 1971;Springer-Verlag, New York/Berlin.
24. Sakai S. On the tensor product of W*-algebras. Amer. J. Math. 90:1968;335-341.
25. Samorodnitskii A. A. Measure Theory. 1990;Izdatelstvo Leningradskogo Universiteta (The Publishing House of the University of Leningrad).
26. Semadeni Z. Banach Spaces of Continuous Functions. Monografie Matematyczne. 55:1971;PWN, Warsaw.
27. Stinespring W. F. Positive functions on C*-algebras. Proc. Amer. Math. Soc. 6:1955;211-216.
28. Stratila S. Modular Theory in Operator Algebras. 1981;Editura Academiei/Abacus Press, Tunbridge Wells.
29. Stratila S., Voiculescu D., Zsidó L. On crossed products, I. Rev. Roumaine Math. Pures Appl. 21:1976;1411-1449.
30. Stratila S., Zsidó L. Lectures on von Neumann Algebras. 1979;Editura Academiei/Abacus Press, Tunbridge Wells.
31. Stratila S., Zsidó L. An algebraic reduction theory for W*-algebras, I. J. Funct. Anal. 11:1972;295-313.
32. Stratila S., Zsidó L. An algebraic reduction theory for W*-algebras II. Rev. Roumaine Math. Pures Appl. 18:1973;407-460.
33. Takesaki M. On the direct product of W*-factors. Tôhoku Math. J. 10:1958;116-119.
34. Wegge-Olsen N. E. K-Theory and C*-Algebras. 1993;Oxford Univ. Press, London.
35. Zsidó L. Reduction theory for W*-algebras. Theory of Operators and Operator Algebras. 1973;Editura Academiei, Bucharest. p. 131-261.
36. Zsidó L. Topological decompositions of W*-algebras, I, II. Stud. Cerc. Mat. 26:1973;859-945.