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 note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Several corollaries and illustrating examples are provided.

Keywords: skew symmetric operator, complex symmetric operator, spect\-rum

MSC numbers: Primary 47A10, 47B99; Secondary 47A05