On m-complex symmetric weighted shift operators on C^n
In this paper we study m-complex symmetric weighted shift operators on C^n. Let T be the (backward) weighted shift on C^n for some n >=2 . We consider when T and T_a (the matrix of entries the moduli of those of T) are both m-complex symmetric with the (same) standard conjugation C, give as well some unitary operators useful in the study, and generalize to upper triangular matrices. Also, we show that if T is 2k-complex symmetric with the standard conjugation C for some k in N with k < n, then T is (2k-1)-complex symmetric with the conjugation C.
Linear Algebra and its Applications
Exner, George R.; Jin, Jooyoung; Jung, Il Bong; and Lee, Ji Eun. "On m-complex symmetric weighted shift operators on C^n." (2020) : 130-153.