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A question of Toeplitz operators on the harmonic Bergman space. (English) Zbl 1143.47018
If an analytic and a co-analytic Toeplitz operator on harmonic Bergman space commute, B. R. Choe and Y. J. Lee [Mich. Math. J. 46, No. 1, 163–174 (1999; Zbl 0969.47023)] posed the question whether then one of their symbols must be constant. The author shows that the answer is yes if one of their symbols is bounded.

MSC:
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
30H05 Spaces of bounded analytic functions of one complex variable
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[1] Axler, S.; Shields, A.L., Algebras generated by analytic and harmonic functions, Indiana univ. math. J., 36, 631-638, (1987) · Zbl 0616.46048
[2] Choe, B.R.; Lee, Y.J., Commuting Toeplitz operators on the harmonic Bergman space, Michigan math. J., 46, 163-174, (1999) · Zbl 0969.47023
[3] Choe, B.R.; Lee, Y.J., Commutants of analytic Toeplitz operators on the harmonic Bergman space, Integral equations operator theory, 50, 559-564, (2004) · Zbl 1088.47016
[4] Guo, K.; Zheng, D., Toeplitz algebra and Hankel algebra on the harmonic Bergman space, J. math. anal. appl., 276, 213-230, (2002) · Zbl 1030.47020
[5] Ross, W.T.; Shapiro, H.S., Generalized analytic continuation, Univ. lecture ser., vol. 25, (2002), Amer. Math. Soc. · Zbl 1009.30002
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