Ranks of complex skew symmetric operators and applications to Toeplitz operators

Yong Chen; Hyungwoon Koo; Young Joo Lee

doi:10.1016/j.jmaa.2015.01.005

Ranks of complex skew symmetric operators and applications to Toeplitz operators

Yong Chen, Hyungwoon Koo, Young Joo Lee

Research output: Contribution to journal › Article › peer-review

11 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 language	English
Pages (from-to)	734-747
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	425
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2015.01.005
Publication status	Published - 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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10.1016/j.jmaa.2015.01.005

Cite this

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title = "Ranks of complex skew symmetric operators and applications to Toeplitz operators",

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.",

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doi = "10.1016/j.jmaa.2015.01.005",

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AU - Chen, Yong

AU - Koo, Hyungwoon

AU - Lee, Young Joo

N1 - 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.

PY - 2015/5/15

Y1 - 2015/5/15

N2 - 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.

AB - 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.

KW - Complex skew symmetric operators

KW - Rank

KW - Toeplitz operators

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U2 - 10.1016/j.jmaa.2015.01.005

DO - 10.1016/j.jmaa.2015.01.005

M3 - Article

AN - SCOPUS:84922920409

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VL - 425

SP - 734

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Ranks of complex skew symmetric operators and applications to Toeplitz operators

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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