In this paper, we study conjugation matrices and complex symmetric operator matrices. In particular, we investigate conditions for 2 * 2 operator matrices to be conjugations or complex symmetric on H+H. Using these results, we provide examples of conjugation matrices and complex symmetric operators. Finally, we apply the main results to block Toeplitz operators and completion problems.
- Conjugation matrices
- Primary: 47A05
- Secondary: 47B35
- block Toeplitz operators
- complex symmetric operator matrices