Integral Equations and Operator Theory

, Volume 60, Issue 1, pp 89–132 | Cite as

Commutative C*-Algebras of Toeplitz Operators on the Unit Ball, II. Geometry of the Level Sets of Symbols

Article

Abstract.

In the first part [16] of this work, we described the commutative C*-algebras generated by Toeplitz operators on the unit ball \({\mathbb{B}}^{n}\) whose symbols are invariant under the action of certain Abelian groups of biholomorphisms of \({\mathbb{B}}^{n}\). Now we study the geometric properties of these symbols. This allows us to prove that the behavior observed in the case of the unit disk (see [3]) admits a natural generalization to the unit ball \({\mathbb{B}}^{n}\). Furthermore we give a classification result for commutative Toeplitz operator C*-algebras in terms of geometric and “dynamic” properties of the level sets of generating symbols.

Mathematics Subject Classification (2000).

Primary 47B35 Secondary 47L80, 32A36, 32M15, 53C12, 53C55 

Keywords.

Toeplitz operator Bergman space commutative C*-algebra unit ball Abelian groups of biholomorphisms flat parallel submanifold Lagrangian submanifold Riemannian foliation totally geodesic foliation 

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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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