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)

Abstract

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
Volume425
Issue number2
DOIs
Publication statusPublished - 2015 May 15

Fingerprint

Electric commutators
Symmetric Operator
Toeplitz Operator
Skew
Finite Rank
Hilbert spaces
Commutator
Mathematical operators
Odd
Bergman Space
Separable Hilbert Space
Ball
Integer

Keywords

  • Complex skew symmetric operators
  • Rank
  • Toeplitz operators

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Ranks of complex skew symmetric operators and applications to Toeplitz operators. / Chen, Yong; Koo, Hyung Woon; Lee, Young Joo.

In: Journal of Mathematical Analysis and Applications, Vol. 425, No. 2, 15.05.2015, p. 734-747.

Research output: Contribution to journalArticle

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