Properties of m-complex symmetric operators

Muneo Cho, Eungil Ko, Ji Eun Lee



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.


Conjugation; $m$-Complex symmetric operator; Nilpotent perturbations ; Decomposable ; Weyl type theorems

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