On $m$-skew complex symmetric operators

Li, Haiying ¹ ; Wang, Yaru ¹

¹ School of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, Henan, P. R. China

Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 6, p. 734-745.

Résumé

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.

Détail

DOI : 10.22436/jnsa.011.06.01

Classification : 47A11, 47B25
Keywords: \(m\)-skew complex symmetric operator, conjugation, spectral

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