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 theoremsAbstract
In this paper, we study several properties of $m$-complex symmetric operators. In particular,
we prove that if $T\in{\cal L(H)}$ 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.
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