Commutators of Complex Symmetric Operators

Authors

  • Rui Dou
  • Xiaolong Ruan
  • Sen Zhu

DOI:

https://doi.org/10.4208/cmr.2024-0053

Keywords:

Complex symmetric operators, commutators, skew symmetric operators.

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.

Published

2025-03-31

Issue

Section

Articles