(untitled) (Communications in Mathematical Research, 2025)
Let C be a conjugation on a separable complex Hilbert space H. An operator T on 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.