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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

$ C\sp{\ast} $-algebras of multivariable Wiener-Hopf operators


Authors: Paul S. Muhly and Jean N. Renault
Journal: Trans. Amer. Math. Soc. 274 (1982), 1-44
MSC: Primary 46L05; Secondary 45E10, 47B35
MathSciNet review: 670916
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Abstract: The $ {C^ \ast }$-algebra $ \mathfrak{W}$ generated by the Wiener-Hopf operators defined over a subsemigroup of a locally compact group is shown to be the image of a groupoid $ {C^ \ast }$-algebra under a suitable representation. When the subsemigroup is either a polyhedral cone or a homogeneous, self-dual cone in an Euclidean space, this representation may be used to show that $ \mathfrak{W}$ is postliminal and to find a composition series with very explicit subquotients. This yields a concrete parameterization of the spectrum of $ \mathfrak{W}$ and exhibits the topology on it.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0670916-3
PII: S 0002-9947(1982)0670916-3
Article copyright: © Copyright 1982 American Mathematical Society