Toeplitz algebra of bounded symmetric domains: A quantum harmonic analysis approach via localization

2025/02/05 by Vishwa Dewage, Dewage, Vishwa · 1 citation
Mathematics · Physics and Astronomy · #22D25 #30H20 #47B35 #47L80 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Waves and Solitons #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2502.03625

openalex publication_date 2025/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that Toeplitz operators are norm dense in the Toeplitz algebra \mathfrakT(L^∞) over the weighted Bergman space A²_ν(Ω) of a bounded symmetric domain Ω⊂ℂⁿ. Our methods use representation theory, quantum harmonic analysis, and weakly-localized operators. Additionally, we note that the set of all α-weakly-localized operators form a self-adjoint algebra, containing the set of all Toeplitz operators, whose norm closure coincides with the Toeplitz algebra.

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