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Proceedings of the American Mathematical Society

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On the type of Wiener-Hopf $ C\sp *$-algebras


Author: Albert Jeu-Liang Sheu
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1990-1010001-4
Keywords: Wiener-Hopf operators, $ {C^*}$-algebras, type of $ {C^*}$-algebras, groupoid $ {C^*}$-algebras
Article copyright: © Copyright 1990 American Mathematical Society