On \(m\)-skew complex symmetric operators


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


MSC


References