Ting Ting Zhou, Bin Liang. Source: Annals of Functional Analysis, Volume 10, Number 3, 350--356.Abstract:
An operator $T\in \mathcal{B}(\mathcal{H})$ is complex-symmetric if there exists a conjugate-linear, isometric involution $C:\mathcal{H}\longrightarrow\mathcal{H}$ so that $CTC=T^{*}$ . In this note, we prove that on finite-dimensional Hilbert space $\mathbb{C}^{n}$ with $n\geq 3$ , noncomplex symmetric operators are dense in $\mathcal{B}(\mathbb{C}^{n})$ .