The spectral properties of ... formula ...-complex symmetric operators

摘要

In this paper, we introduce the class of [m]-complex symmetric operators and study various properties of this class. In particular, we show that if T is an [m]-complex symmetric operator, then Tⁿ is also an [m]-complex symmetric operator for any n ∈ ℕ. In addition, we prove that if T is an [m]-complex symmetric operator, then σa(T), σSVEP(T), σβ(T), and σ(β)ϵ(T) are symmetric about the real axis. Finally, we investigate the stability of an [m]-complex symmetric operator under perturbation by nilpotent operators commuting with T.