On \(m\)-skew complex symmetric operators

Volume 11, Issue 6, pp 734--745 http://dx.doi.org/10.22436/jnsa.011.06.01 Publication Date: April 06, 2018       Article History

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.


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