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Proceedings of the American Mathematical Society

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On the smoothed Toeplitz extensions and $ K$-theory


Author: Ronghui Ji
Journal: Proc. Amer. Math. Soc. 109 (1990), 31-38
MSC: Primary 46L80; Secondary 19K99, 46M20
DOI: https://doi.org/10.1090/S0002-9939-1990-1002159-8
MathSciNet review: 1002159
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Abstract: We construct a smoothed version of the Toeplitz extension for a $ {C^ * }$-dynamical system $ (A,\alpha ,{\mathbf{R}})$. It defines a Thom class $ [\tau ]$ in $ K{K^1}(A,A{ \times _\alpha }{\mathbf{R}})$. The Wiener-Hopf-Rieffel extension for $ (A,\alpha ,{\mathbf{R}})$ is shown to be a smoothed Toeplitz extension which is the $ KK$-inverse of $ [\tau ]$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1002159-8
Keywords: Toeplitz extension, $ {C^ * }$-algebras, Thom class, $ K$-theory, $ {C^ * }$-dynamical systems
Article copyright: © Copyright 1990 American Mathematical Society

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