Integral Equations and Operator Theory

, Volume 63, Issue 4, pp 547–555

Finite-Rank Products of Toeplitz Operators in Several Complex Variables


DOI: 10.1007/s00020-009-1661-6

Cite this article as:
Le, T. Integr. equ. oper. theory (2009) 63: 547. doi:10.1007/s00020-009-1661-6


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.


Toeplitz operatorweighted Bergman spacefinite-rank product

Mathematics Subject Classification (2000).


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© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada