Bulletin of the
Korean Mathematical Society BKMS

An operator $T\in{\mathcal L(\mathcal H)}$ is said to be skew complex symmetric if there exists a conjugation $C$ on ${\mathcal H}$ such that $T= -CT^{\ast}C$. In this paper, we study properties of skew complex symmetric operators including spectral connections, Fredholmness, and subspace-hypercyclicity between skew complex symmetric operators and their adjoints. Moreover, we consider Weyl type theorems and Browder type theorems for skew complex symmetric operators.

Keywords: skew complex symmetric operator, subspace-hypercyclicity, Weyl type theorems

MSC numbers: Primary 47A10, 47A53