On m-complex symmetric weighted shift operators on Cn

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 is an element of N with k < n, then T is (2k - 1)-complex symmetric with the conjugation C. (C) 2020 Elsevier Inc. All rights reserved.