Properties of m-complex symmetric operators
DOI:
https://doi.org/10.24193/subbmath.2017.2.09Keywords:
Conjugation, m-complex symmetric operator, nilpotent perturbations, decomposable, Weyl type theorems.Abstract
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.
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