Document Type: Original Article
Department of Mathematics and Physics
Faculty of Electrical Engineering and Information Technology
Ss. Cyril and Methodius University in Skopje
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.