Commuting Toeplitz operators on the polydisk

Choe, Boo; Koo, Hyungwoon; Lee, Young

doi:10.1090/S0002-9947-03-03430-5

Commuting Toeplitz operators on the polydisk
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by Boo Rim Choe, Hyungwoon Koo and Young Joo Lee PDF

Trans. Amer. Math. Soc. 356 (2004), 1727-1749 Request permission

Abstract:

We obtain characterizations of (essentially) commuting Toeplitz operators with pluriharmonic symbols on the Bergman space of the polydisk. We show that commuting and essential commuting properties are the same for dimensions bigger than 2, while they are not for dimensions less than or equal to 2. Also, the corresponding results for semi-commutators are obtained.

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