Finite Sums of Toeplitz Products on the Polydisk |
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Authors: | Boo Rim Choe Hyungwoon Koo Young Joo Lee |
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Affiliation: | 1.Department of Mathematics,Korea University,Seoul,South Korea;2.Department of Mathematics,Chonnam National University,Gwangju,South Korea |
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Abstract: | On the Bergman space of the unit polydisk, we study a class of operators which contains sums of finitely many Toeplitz products with pluriharmonic symbols. We give characterizations of when an operator in that class has finite rank or is compact. As one of applications we show that sums of a certain number, depending on and increasing with the dimension, of semicommutators of Toeplitz operators with pluriharmonic symbols cannot be compact without being the zero operator. |
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