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Transactions of the American Mathematical Society

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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
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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 $.


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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

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