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Integral Equations and Operator Theory

, Volume 50, Issue 4, pp 559–564 | Cite as

Commutants of Analytic Toeplitz Operators on the Harmonic Bergman Space

Short Communication

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.

Mathematics Subject Classification (2000).

Primary 47B35 

Keywords.

Commutant Toeplitz operator harmonic Bergman space 

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Copyright information

© Birkhäuser Verlag, Basel 2004

Authors and Affiliations

  1. 1.Department of MathematicsKorea UniversitySeoulKorea
  2. 2.Department of MathematicsMokpo National UniversityChonnamKorea

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