Integral Equations and Operator Theory

, Volume 63, Issue 4, pp 547–555

Finite-Rank Products of Toeplitz Operators in Several Complex Variables

Article

Abstract.

For any α > −1, let A2α be the weighted Bergman space on the unit ball corresponding to the weight (1 – |z|2)α. We show that if all except possibly one of the Toeplitz operators \(T_{f_{1} },\ldots,T_{f_{r}}\) are diagonal with respect to the standard orthonormal basis of A2α and \(T_{f_{1}} \cdots T_{f_{r}}\) has finite rank, then one of the functions \(f_{1} ,\ldots, f_{r}\) must be the zero function.

Keywords.

Toeplitz operator weighted Bergman space finite-rank product 

Mathematics Subject Classification (2000).

47B35 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada

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