Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Finite projections in tensor product von Neumann algebras


Author: George A. Elliott
Journal: Trans. Amer. Math. Soc. 212 (1975), 47-60
MSC: Primary 46L10
DOI: https://doi.org/10.1090/S0002-9947-1975-0377535-3
MathSciNet review: 0377535
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The work of Bures, Moore, Takenouchi, Hill and Størmer on the type classification of infinite tensor products of factors is extended to the nonfactor case.


References [Enhancements On Off] (What's this?)

  • [1] D. J. C. Bures, Certain factors constructed as infinite tensor products, Compositio Math. 15 (1963), 169-191. MR 27 #1809. MR 0151826 (27:1809)
  • [2] -, An extension of Kakutani's theorem on infinite product measures to the tensor product of semifinite $ {w^\ast}$-algebras, Trans. Amer. Math. Soc. 135 (1969), 199-212. MR 38 #5014. MR 0236719 (38:5014)
  • [3] A. Connes, Une classification des facteurs de type III, Ann. Sci. École Norm. Sup. 6 (1973), 133-252. MR 0341115 (49:5865)
  • [4] J. G. Glimm, Type I $ {C^\ast}$-algebras, Ann. of Math. (2) 73 (1961), 572-612. MR 23 #A2066. MR 0124756 (23:A2066)
  • [5] D. G. B. Hill, $ \sigma $-finite invariant measures on infinite product spaces, Trans. Amer. Math Soc. 153 (1971), 347-370. MR 43 #485. MR 0274725 (43:485)
  • [6] R. R. Kallman, Groups of inner automorphisms of von Neumann algebras, J. Functional Analysis 7 (1971), 43-60. MR 43 #5317. MR 0279596 (43:5317)
  • [7] C. C. Moore, Invariant measures on product spaces, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Vol. II: Contributions to Probability Theory, part 2, Univ. of California Press, Berkeley, Calif., 1967, pp. 447-459. MR 37 #2951. MR 0227366 (37:2951)
  • [8] S. Sakai, On topological properties of $ {W^\ast}$-algebras, Proc. Japan Acad. 33 (1957), 439-444. MR 20 #5437. MR 0098992 (20:5437)
  • [9] E. Størmer, On infinite tensor products of von Neumann algebras, Amer. J. Math. 93 (1971), 810-818. MR 44 #5792. MR 0288596 (44:5792)
  • [10] O. Takenouchi, On type classification of factors constructed as infinite tensor products, Publ. Res. Inst. Math. Sci. Ser. A 4 (1968/69), 467-482. MR 40 #762. MR 0247497 (40:762)
  • [11] M. Takesaki, On the cross-norm of the direct product of $ {C^\ast}$-algebras, Tôhoku Math. J. (2) 16 (1964), 111-122. MR 0165384 (29:2668)
  • [12] -, Tomita's theory of modular Hilbert algebras and its applications, Lecture Notes in Math., vol. 128, Springer-Verlag, New York, 1970.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46L10

Retrieve articles in all journals with MSC: 46L10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0377535-3
Keywords: von Neumann algebra, infinite tensor product, finite projection, tensor product projection
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society