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.
Original language | English |
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Pages (from-to) | 227-255 |
Number of pages | 29 |
Journal | Potential Analysis |
Volume | 31 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2009 Sept |
Bibliographical note
Funding Information:The first two authors were supported by the Korea Science and Engineering Foundation Grant funded by the Korean Government (KOSEF R01-2008-000-20206-0) and the third author was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-313-C00034).
Keywords
- Bergman space
- Finite rank operators
- Polydisk
- Toeplitz operators
ASJC Scopus subject areas
- Analysis