Reducible and irreducible approximation of complex symmetric operators

Abstract

This paper aims to study reducible and irreducible approximation in the set $\textsl{CSO}$ of all complex symmetric operators on a separable, complex Hilbert space $\mathcal H$. When ${\rm dim} \mathcal H=\infty$, it is proved that both those reducible ones and those irreducible ones are norm dense in $\textsl{CSO}$. When ${\rm dim} \mathcal H<\infty$, irreducible complex symmetric operators constitute an open, dense subset of $\textsl{CSO}$.