ON SKEW SYMMETRIC OPERATORS WITH EIGENVALUES
An operator T on a complex Hilbert space H is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for 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.