On the smoothed Toeplitz extensions and 𝐾-theory

Ji, Ronghui

doi:10.1090/S0002-9939-1990-1002159-8

On the smoothed Toeplitz extensions and $K$-theory
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Proc. Amer. Math. Soc. 109 (1990), 31-38 Request permission

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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