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On approximately inner automorphisms of certain crossed product $ C\sp *$-algebras


Authors: Marius Dădărlat and Cornel Pasnicu
Journal: Proc. Amer. Math. Soc. 110 (1990), 383-385
MSC: Primary 46L55; Secondary 18F25, 46L40
DOI: https://doi.org/10.1090/S0002-9939-1990-1021897-4
MathSciNet review: 1021897
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be a compact connected topological group having a dense subgroup isomorphic to $ {\mathbf{Z}}$. Let $ C(G)\mathop \rtimes \limits_ \propto {\mathbf{Z}}$ be the crossed product $ {C^ * }$-algebra of $ C(G)$ with $ {\mathbf{Z}}$, where $ {\mathbf{Z}}$ acts on $ G$ by rotations. Automorphisms of $ C(G)\mathop \rtimes \limits_ \propto {\mathbf{Z}}$ leaving invariant the canonical copy of $ C(G)$ are shown to be approximately inner iff they act trivially on $ {K_1}(C(G)\mathop \rtimes \limits_ \propto {\mathbf{Z}})$.


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

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DOI: https://doi.org/10.1090/S0002-9939-1990-1021897-4
Article copyright: © Copyright 1990 American Mathematical Society

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