Spectral theorem approach to commutative C* -algebras generated by Toeplitz operators on the unit ball: quasi-elliptic related cases

2022/11/20 by Grigori Rozenblum, Rozenblum, Grigori, Nikolai Vasilevski +1
Mathematics · #32A36 #47A13 #47B35 #47L80 #Advanced Operator Algebra Research #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2211.11111

openalex publication_date 2022/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider commutative C* -algebras of Toeplitz operators in the weighted Bergman space on the unit ball in ℂⁿ. For the algebras of elliptic type we find a new representation, namely as the algebra of operators which are functions of certain collections of commuting unbounded self-adjoint operators in the Bergman space.

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