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)

 
 

 

The quasi-orbit space of continuous $ C\sp{\ast} $-dynamical systems


Author: Hiroshi Takai
Journal: Trans. Amer. Math. Soc. 216 (1976), 105-113
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9947-1976-0385583-3
MathSciNet review: 0385583
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ (A,G,\alpha )$ be a separable continuous $ {C^\ast}$-dynamical system. Suppose G is amenable and $ \alpha $ is free on the dual  of A. Then the quasi-orbit space $ {({\text{Prim}}\;A/\alpha )^ \sim }$ of the primitive ideal space Prim A of A by $ \alpha $ is homeomorphic to the induced primitive ideal space which is dense in the primitive ideal space Prim $ {C^\ast}(A;\alpha )$ of the $ {C^\ast}$-crossed product $ {C^\ast}(A;\alpha )$ of A by $ \alpha $.


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

  • [1] R. C. Busby and H. A. Smith, Representations of twisted group algebras, Trans. Amer. Math. Soc. 149 (1970), 503-537. MR 41 #9013. MR 0264418 (41:9013)
  • [2] Dang-Ngoc Nghiem and A. Guichardet, Seminar report on $ {C^\ast}$-dynamical systems, Paris, 1973.
  • [3] E. G. Effros and F. Hahn, Locally compact transformation groups and $ {C^\ast}$-algebras, Mem. Amer. Math. Soc. No. 75 (1967). MR 37 #2895. MR 0227310 (37:2895)
  • [4] J. G. Glimm, Families of induced representations, Pacific J. Math. 12 (1962), 885-911. MR 26 #3819. MR 0146297 (26:3819)
  • [5] H. Takai, On a duality for crossed products of $ {C^\ast}$-algebras, CPT-CNRS, Marseille, 1974 (preprint).
  • [6] -, Dualité dans les produits croisés de $ {C^\ast}$-algèbres, C. R. Acad. Sci. Paris Sér. A-B 278 (1974), A1041-A1043.
  • [7] G. Zeller-Meier, Produits croisés d'une $ {C^\ast}$-algèbre par un groupe d'automorphismes, J. Math. Pures Appl. (9) 47 (1968), 101-239. MR 39 #3329. MR 0241994 (39:3329)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46L05

Retrieve articles in all journals with MSC: 46L05


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0385583-3
Keywords: Continuous dynamical system, quasi-orbit space, crossed products
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society