Abstract.
Extending known results for the unit disk, we prove that for the unit ball \({\mathbb{B}}^n\) there exist n+2 different cases of commutative C*-algebras generated by Toeplitz operators, acting on weighted Bergman spaces. In all cases the bounded measurable symbols of Toeplitz operators are invariant under the action of certain commutative subgroups of biholomorphisms of the unit ball.
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This work was partially supported by CONACYT Projects 46936 and 44620, México.
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Quiroga-Barranco, R., Vasilevski, N. Commutative C*-Algebras of Toeplitz Operators on the Unit Ball, I. Bargmann-Type Transforms and Spectral Representations of Toeplitz Operators. Integr. equ. oper. theory 59, 379–419 (2007). https://doi.org/10.1007/s00020-007-1537-6
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DOI: https://doi.org/10.1007/s00020-007-1537-6