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The commutants of analytic Toeplitz operators for several complex variables

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Abstract

It is proved that if φ is a nonconstant bounded analytic function on the unit ball B n and continuous on S n in ℂn, and ψ is a bounded measurable function on S n such that T φ* and T ψ commute, then ψ is the boundary value of an analytic function on B n . In addition, the commutants of two Toeplitz operators are also discussed.

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Authors and Affiliations

  1. Department of Mathematics, Guangzhou University, Guangzhou, 510006, China

    GuangFu Cao & Sui Huang

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  1. GuangFu Cao
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  2. Sui Huang
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Correspondence to GuangFu Cao.

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Cao, G., Huang, S. The commutants of analytic Toeplitz operators for several complex variables. Sci. China Math. 53, 1877–1884 (2010). https://doi.org/10.1007/s11425-010-4023-6

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  • DOI: https://doi.org/10.1007/s11425-010-4023-6

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