Toeplitz operators with symmetric, alternating and anti-symmetric separately radial symbols on the unit ball

2024/03/12 by Armando Sánchez-Nungaray, Sánchez-Nungaray, Armando, José Rosales-Ortega +3
Mathematics · #22E46 #32A36 #32M15 #47B35 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematics and Applications #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2403.08138

openalex publication_date 2024/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider symmetric separately radial (with corresponding group S_n\rtimes \mathbbTⁿ) and alternating separately radial (with corresponding group A_n\rtimes \mathbbTⁿ) symbols, as well as the associated Toeplitz operators on the weighted Bergman spaces on the unit ball on ℂⁿ. Using a purely representation theoretic approach we obtain that the C^*-algebras generated by each family of such Toeplitz operators is commutative. Furthermore, we show that the symmetric separately radial Toeplitz operators are more general than radial Toeplitz operators, i.e., every radial Toeplitz operator is a symmetric separately radial.

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