Ranks of complex skew symmetric operators and applications to Toeplitz operators

Yong Chen, Hyung Woon Koo, Young Joo Lee

Research output: Contribution to journalArticle

4 Citations (Scopus)


We study the rank of complex skew symmetric operators on separable Hilbert spaces. We prove that a finite rank complex skew symmetric operator can't have an odd rank. As applications, we show that any finite rank commutator of two Toeplitz operators on the pluriharmonic Bergman space of the ball can't have an odd rank. We also show that for any positive even integer N, there are two Toeplitz operators whose commutator is exactly of rank N. Also we obtain the similar result for certain truncated Toeplitz operators.

Original languageEnglish
Pages (from-to)734-747
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - 2015 May 15



  • Complex skew symmetric operators
  • Rank
  • Toeplitz operators

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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