Year: 2025
Author: Rui Dou, Xiaolong Ruan, Sen Zhu
Communications in Mathematical Research , Vol. 41 (2025), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2024-0053
Communications in Mathematical Research , Vol. 41 (2025), Iss. 1 : pp. 59–68
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Complex symmetric operators commutators skew symmetric operators.