Spectral theorem approach to commutative \(C^\ast\)-algebras generated by Toeplitz operators on the unit ball: quasi-elliptic related cases

DOI10.1016/j.jmaa.2023.127543arXiv2211.11111WikidataQ123162876 ScholiaQ123162876MaRDI QIDQ6136373

Nikolai L. Vasilevski, Grigori Rozenblum

Publication date: 29 August 2023

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.11111

zbMATH Keywords

Bergman spacesspectral representationToeplitz operatorscommutative algebras

Mathematics Subject Classification ID

Special classes of linear operators (47Bxx) Linear spaces and algebras of operators (47Lxx) Holomorphic functions of several complex variables (32Axx)

Cites Work

• Toeplitz operators defined by sesquilinear forms: Bergman space case
• On algebras generated by Toeplitz operators and their representations
• Eigenvalue characterization of radial operators on weighted Bergman spaces over the unit ball
• Quasi-radial quasi-homogeneous symbols and commutative Banach algebras of Toeplitz operators
• Moment maps of abelian groups and commuting Toeplitz operators acting on the unit ball
• Commutative algebras of Toeplitz operators on the Bergman space revisited: spectral theorem approach
• Toeplitz operators, \(\mathbb{T}^m\)-invariance and quasi-homogeneous symbols
• Algebras of Toeplitz operators on the \(n\)-dimensional unit ball
• On the structure of commutative Banach algebras generated by Toeplitz operators on the unit ball. Quasi-elliptic case. I: Generating subalgebras.
• Commutative algebras of Toeplitz operators on the Bergman space
• Commutative \(C^*\)-algebras of Toeplitz operators on the unit ball. I: Bargmann-type transforms and spectral representations of Toeplitz operators
• Commutative \(C^{\ast}\)-algebras of Toeplitz operators and quantization on the unit disk
• Bergman-Toeplitz operators: Radial component influence
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