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Commutants of Analytic Toeplitz Operators on the Harmonic Bergman Space

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Abstract.

We study the commuting problem for Toeplitz operators on the harmonic Bergman space of the unit disk. We show that an analytic Toeplitz operator and a co-analytic Toeplitz operator with certain noncyclicity hypothesis can commute only when one of their symbols is constant. We also obtain analogous results for semi-commutants.

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Authors and Affiliations

  1. Department of Mathematics, Korea University, Seoul, 136-713, Korea

    Boo Rim Choe

  2. Department of Mathematics, Mokpo National University, Chonnam, 534-729, Korea

    Young Joo Lee

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  1. Boo Rim Choe
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  2. Young Joo Lee
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Correspondence to Boo Rim Choe.

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Choe, B.R., Lee, Y.J. Commutants of Analytic Toeplitz Operators on the Harmonic Bergman Space. Integr. equ. oper. theory 50, 559–564 (2004). https://doi.org/10.1007/s00020-004-1338-0

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  • DOI: https://doi.org/10.1007/s00020-004-1338-0

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