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Commutative Banach Algebras Generated by Toeplitz Operators on the Bergman Space (2206.11557v1)
Published 23 Jun 2022 in math.FA and math.OA
Abstract: We present and study commutative Banach algebras generated by Toeplitz operators with generalized quasi-radial pseudo-homogeneous symbols acting on the Bergman space over the unit ball. We develop the Gelfand theory of these algebras and give some structural information about them. In particular, we provide a description of the radical of these algebras. This paper generalizes and completes the results from previous works related to Toeplitz operators with quasi-radial quasi-homogeneous symbols.