Integral Equations and Operator Theory

, Volume 59, Issue 3, pp 379–419 | Cite as

Commutative C*-Algebras of Toeplitz Operators on the Unit Ball, I. Bargmann-Type Transforms and Spectral Representations of Toeplitz Operators



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.

Mathematics Subject Classification (2000).

Primary 47B35 Secondary 47L80, 32A36 


Toeplitz operator Bergman space commutative C*-algebra unit ball commutative groups of biholomorphisms 


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Copyright information

© Birkhaueser 2007

Authors and Affiliations

  1. 1.Centro de Investigación en MatemáticasGuanajuato, Gto.México
  2. 2.Departamento de MatemáticasCINVESTAVMéxico, D.F.México

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