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 - <p style="text-align: justify;">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.</p>