Toeplitz C^*-Algebras on Boundary Orbits of Symmetric Domains

2019/12/02 by Gadadhar Misra, Misra, Gadadhar, Harald Upmeier +1
Mathematics · #32M15 #46E22 #Advanced Operator Algebra Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #math.AG #math.FA #msc:32M15 #msc:46E22

paper · pdf · doi:10.48550/arxiv.1912.00674

22 pages

arxiv created 2019/12/02 · openalex publication_date 2019/12/02 · arxiv updated 2019/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Toeplitz operators on Hilbert spaces of holomorphic functions on symmetric domains, and more generally on certain algebraic subvarieties, determined by integration over boundary orbits of the underlying domain. The main result classifies the irreducible representations of the Toeplitz C^*-algebra generated by Toeplitz operators with continuous symbol. This relies on the limit behavior of "hypergeometric" measures under certain peaking functions.

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