Toeplitz operators on symmetric Siegel domains
In this paper, the structure theory for Toeplitz \(C^*\)-algebras over bounded symmetric domains in \({\mathbb{C}}^ n\) [cf. \textit{H. Upmeier}, Ann. Math., II. Ser. 119, 549-576 (1984; Zbl 0549.46031)] is applied to study smooth Toeplitz operators on the distinguished boundary \(\Sigma\) of a symmetric Siegel domain D. As the main result, it is shown that the \(C^*\)-algebra \({\mathcal T}_{\Sigma}\) generated by these operators is solvable of length \(r=rank(D)\) and that its irreducible representations correspond to the boundary components of D. This applies in particular to Wiener-Hopf operators on self-dual homogeneous cones, first studied by \textit{P. S. Muhly} and \textit{J. N. Renault} [Trans. Am. Math. Soc. 274, 1- 44 (1982; Zbl 0509.46049)].
structure theory for Toeplitz \(C^*\)-algebras over bounded symmetric domains
Wiener-Hopf operators on self-dual homogeneous cones
scientific article; zbMATH DE number 3901472
scientific article