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.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 1053-1058
- MSC: Primary 46L55; Secondary 47B35, 47D99
- DOI: https://doi.org/10.1090/S0002-9939-1990-1010001-4
- MathSciNet review: 1010001