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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.

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
30H05 Spaces of bounded analytic functions of one complex variable
Full Text: DOI
[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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