Finite sums of Toeplitz products on the polydisk

Boo Rim Choe, Hyungwoon Koo, Young Joo Lee

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)227-255
Number of pages29
JournalPotential Analysis
Volume31
Issue number3
DOIs
Publication statusPublished - 2009 Sep 1

Keywords

  • Bergman space
  • Finite rank operators
  • Polydisk
  • Toeplitz operators

ASJC Scopus subject areas

  • Analysis

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