Commutative Toeplitz Banach algebras on the ball and quasi-nilpotent group action

DOI10.1007/S00020-011-1927-7zbMath1263.47032OpenAlexW2051380674MaRDI QIDQ421101

Wolfram Bauer, Nikolai L. Vasilevski

Publication date: 23 May 2012

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00020-011-1927-7

zbMATH Keywords

commutative Banach algebraweighted Bergman spacesToeplitz operatorsquasi-homogeneousquasi-nilpotent

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Bergman spaces of functions in several complex variables (32A36) Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) (47L80)

Related Items (10)

Commutative Toeplitz algebras and their Gelfand theory: old and new results ⋮ Construction of some classes of commutative Banach and \(C^{\star}\)-algebras of Toeplitz operators ⋮ Commutative algebras generated by Toeplitz operators on the unit sphere ⋮ On the structure of a commutative Banach algebra generated by Toeplitz operators with quasi-radial quasi-homogeneous symbols ⋮ Toeplitz Operators with $$\mathbb {T}_q^m$$ -Invariant Symbols on Some Weakly Pseudoconvex Domains ⋮ On Toeplitz Operators with Quasi-radial and Pseudo-homogeneous Symbols ⋮ On the structure of commutative Banach algebras generated by Toeplitz operators on the unit ball. Quasi-elliptic case. I: Generating subalgebras. ⋮ Algebraic properties of quasihomogeneous and separately quasihomogeneous Toeplitz operators on the pluriharmonic Bergman space ⋮ Moment maps of abelian groups and commuting Toeplitz operators acting on the unit ball ⋮ On the structure of commutative Banach algebras generated by Toeplitz operators on the unit ball. Quasi-elliptic case. II: Gelfand theory

Cites Work

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• Quasi-radial quasi-homogeneous symbols and commutative Banach algebras of Toeplitz operators
• Commutative \(C^*\)-algebras of Toeplitz operators on the unit ball. I: Bargmann-type transforms and spectral representations of Toeplitz operators
• Commutative \(C^*\)-algebras of Toeplitz operators on the unit ball. II: Geometry of the level sets of symbols
• Commutative \(C^{\ast}\)-algebras of Toeplitz operators and quantization on the unit disk
• Banach Algebras of Commuting Toeplitz Operators on the Unit Ball via the Quasi-hyperbolic Group

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