In this paper, first we characterize the spectra of skew $[m,C]$-symmetric operators and we also prove that if operators $T$ and $S$ are $C$-doubly commuting operators, $T$ is a skew $[m,C]$-symmetric operator and $Q$ is an $n$-nilpotent operator, then $T+Q$ is a skew $[m+2n-2,C]$-symmetric operator. Finally, we show that if $T$ is skew $[m,C]$-symmetric and $S$ is $[n,D]$-symmetric, then $T \otimes S$ is skew $[m+n-1, C \otimes D]$-symmetric.
"On skew $[m,C]$-symmetric operators." Adv. Oper. Theory 2 (4) 468 - 474, Autumn 2017. https://doi.org/10.22034/aot.1703-1147