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Volume 41, Issue 1
Commutators of Complex Symmetric Operators

Rui Dou, Xiaolong Ruan & Sen Zhu

DOI: 10.4208/cmr.2024-0053

Commun. Math. Res., 41 (2025), pp. 59-68.

Published online: 2025-03

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  • Abstract

Let $C$ be a conjugation on a separable complex Hilbert space $\mathcal{H}.$ An operator $T$ on $\mathcal{H}$ is said to be $C$-symmetric if $CTC = T^∗,$ and $T$ is said to be $C$-skew symmetric if $CTC=−T^∗$. It is proved in this paper that each $C$-skew symmetric operator can be written as the sum of two commutators of $C$-symmetric operators.

  • Keywords

Complex symmetric operators, commutators, skew symmetric operators.

  • AMS Subject Headings

Primary 47B47, 47B99, Secondary 47L05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-41-59, author = {Dou , RuiRuan , Xiaolong and Zhu , Sen}, title = {Commutators of Complex Symmetric Operators}, journal = {Communications in Mathematical Research }, year = {2025}, volume = {41}, number = {1}, pages = {59--68}, abstract = {

Let $C$ be a conjugation on a separable complex Hilbert space $\mathcal{H}.$ An operator $T$ on $\mathcal{H}$ is said to be $C$-symmetric if $CTC = T^∗,$ and $T$ is said to be $C$-skew symmetric if $CTC=−T^∗$. It is proved in this paper that each $C$-skew symmetric operator can be written as the sum of two commutators of $C$-symmetric operators.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2024-0053}, url = {http://global-sci.org/intro/article_detail/cmr/23931.html} }
TY - JOUR T1 - Commutators of Complex Symmetric Operators AU - Dou , Rui AU - Ruan , Xiaolong AU - Zhu , Sen JO - Communications in Mathematical Research VL - 1 SP - 59 EP - 68 PY - 2025 DA - 2025/03 SN - 41 DO - http://doi.org/10.4208/cmr.2024-0053 UR - https://global-sci.org/intro/article_detail/cmr/23931.html KW - Complex symmetric operators, commutators, skew symmetric operators. AB -

Let $C$ be a conjugation on a separable complex Hilbert space $\mathcal{H}.$ An operator $T$ on $\mathcal{H}$ is said to be $C$-symmetric if $CTC = T^∗,$ and $T$ is said to be $C$-skew symmetric if $CTC=−T^∗$. It is proved in this paper that each $C$-skew symmetric operator can be written as the sum of two commutators of $C$-symmetric operators.

Dou , RuiRuan , Xiaolong and Zhu , Sen. (2025). Commutators of Complex Symmetric Operators. Communications in Mathematical Research . 41 (1). 59-68. doi:10.4208/cmr.2024-0053
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