Ranks of complex skew symmetric operators and applications to Toeplitz operators

Yong Chen, Hyungwoon Koo, Young Joo Lee

Research output: Contribution to journalArticlepeer-review

10 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

Bibliographical note

Funding Information:
The first author was supported by NSFC (Nos. 11471113 , 11201274 ), Tianyuan Foundation of China (No. 11226114 ) and ZJNSFC (Nos. LY14A010013 , LQ12A01004 ), and the second author was supported by NRF of Korea ( 2014R1A1A2054145 ). Also, the third author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2014R1A1A4A01003810 ).

Publisher Copyright:
© 2015 Elsevier Inc.

Keywords

  • Complex skew symmetric operators
  • Rank
  • Toeplitz operators

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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