Commutative C*-Algebras of Toeplitz Operators on Complex Projective Spaces

Article

Abstract

We prove the existence of commutative C*-algebras of Toeplitz operators on every weighted Bergman space over the complex projective space \({{\mathbb{P}^n}\mathbb{(C)}}\). The symbols that define our algebras are those that depend only on the radial part of the homogeneous coordinates. The algebras presented have an associated pair of Lagrangian foliations with distinguished geometric properties and are closely related to the geometry of \({{\mathbb{P}^n}\mathbb{(C)}}\).

Mathematics Subject Classification (2010)

Primary 47B35 Secondary 32A36 32M15 53C12 

Keywords

Toeplitz operator Bergman space complex projective space commutative C*-algebra Lagrangian foliation Abelian group 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Centro de Investigación en MatemáticasGuanajuatoMexico

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