On the type of Wiener-Hopf 𝐶*-algebras

Sheu, Albert Jeu-Liang

doi:10.1090/S0002-9939-1990-1010001-4

On the type of Wiener-Hopf $C^ *$-algebras
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by Albert Jeu-Liang Sheu PDF

Proc. Amer. Math. Soc. 109 (1990), 1053-1058 Request permission

Abstract:

In this paper, we show that if the positive cone $P$ of a locally compact group $G$ does not satisfy a regularity condition then the corresponding Wiener-Hopf ${C^ * }$-algebra $\mathcal {W}(P)$ is not of type I while the converse does not hold, and that if ${C^ * }(G)$ is not of type I then neither is $\mathcal {W}(P)$. Thus a conjecture and a question, both proposed by P. Muhly and J. Renault in their important systematic treatment of general Wiener-Hopf ${C^ * }$-algebras using groupoid ${C^*}$-algebras, are settled.

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Index theory and Toeplitz algebras on certain cones in

A groupoid approach to

-algebras

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