Properties of m-complex symmetric operators - CHŌ, Muneo; KO, Eungil; LEE, Ji Eun (Studia Universitatis Babeș-Bolyai Mathematica, 2017)
In this paper, we study several properties of m-complex symmetric operators. In particular, we prove that if T ∈ L(H) is an m-complex symmetric operator and N is a nilpotent operator of order n > 2 with TN = NT , then T +N is a (2n+m−2)-complex symmetric operator. Moreover, we investigate the decomposability of T + A and TA where T is an m-complex symmetric operator and A is an algebraic operator. Finally, we provide various spectral relations of such operators. As some applications of these results, we discuss Weyl type theorems for such operators. Mathematics Subject Classification (2010): 47A11, 47B25.