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April 2019 Toeplitz operators on Jordan–Kepler varieties
Harald Upmeier
Banach J. Math. Anal. 13(2): 314-337 (April 2019). DOI: 10.1215/17358787-2018-0038

Abstract

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.

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Harald Upmeier. "Toeplitz operators on Jordan–Kepler varieties." Banach J. Math. Anal. 13 (2) 314 - 337, April 2019. https://doi.org/10.1215/17358787-2018-0038

Information

Received: 6 September 2018; Accepted: 11 November 2018; Published: April 2019
First available in Project Euclid: 1 February 2019

zbMATH: 07045461
MathSciNet: MR3927876
Digital Object Identifier: 10.1215/17358787-2018-0038

Subjects:
Primary: 39B82
Secondary: 32025 , 46C05

Keywords: algebraic varieties , Hilbert quotient modules , symmetric domains , Toeplitz operators

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 2 • April 2019
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