# On $m$-skew complex symmetric operators

Volume 11, Issue 6, pp 734--745 Publication Date: April 06, 2018       Article History
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### Authors

Haiying Li - School of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, Henan, P. R. China
Yaru Wang - School of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, Henan, P. R. China

### Abstract

In this paper, the definition of $m$-skew complex symmetric operators is introduced. Firstly, we prove that $\Delta_{m}^{-}(T)$ is complex symmetric with the conjugation $C$ and give some properties of $\Delta_{m}^{-}(T)$. Secondly, let $T$ be $m$-skew complex symmetric with conjugation $C$, if $n$ is odd, then $T^{n}$ is $m$-skew complex symmetric with conjugation $C$; if $n$ is even, with the assumption $T^{*}CTC=CTCT^{*}$, then $T^{n}$ is $m$-complex symmetric with conjugation $C$. Finally, we give some properties of $m$-skew complex symmetric operators.

### Keywords

• $m$-skew complex symmetric operator
• conjugation
• spectral

•  47A11
•  47B25

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