Journal of the
Korean Mathematical Society JKMS

An operator $T$ on a complex Hilbert space $\mathcal{H}$ is called skew symmetric if $T$ can be represented as a skew symmetric matrix relative to some orthonormal basis for $\mathcal{H}$. In this paper, we study skew symmetric operators with eigenvalues. First, we provide an upper-triangular operator matrix representation for skew symmetric operators with nonzero eigenvalues. On the other hand, we give a description of certain skew symmetric triangular operators, which is based on the geometric relationship between eigenvectors.

Keywords: skew symmetric operator, complex symmetric operator, eigenvalue, triangular operator

MSC numbers: Primary 47A66, 47A65; Secondary 47A45