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Toeplitz operators on Jordan-Kepler varieties. (English) Zbl 1447.47033
Summary: We study Toeplitz operators on Hilbert spaces of holomorphic functions on algebraic varieties, the generalized Kepler varieties defined in Jordan theoretic terms. Using the fine analysis of the reproducing kernel function, we construct and classify the irreducible representations of the \(C^{*}\)-algebra generated by these operators (with smooth symbols). The limit behavior of Bergman-type measures under peaking functions is of special importance.

MSC:
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
47C15 Linear operators in \(C^*\)- or von Neumann algebras
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