𝐶*-algebras of multivariable Wiener-Hopf operators

Muhly, Paul S.; Renault, Jean N.

doi:10.1090/S0002-9947-1982-0670916-3

$C^{\ast }$-algebras of multivariable Wiener-Hopf operators
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by Paul S. Muhly and Jean N. Renault

Trans. Amer. Math. Soc. 274 (1982), 1-44

DOI: https://doi.org/10.1090/S0002-9947-1982-0670916-3

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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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