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.
Bibliographical noteFunding Information:
This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education [grant number 2016R1D1A1B03931937]. The second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology [grant number 2016R1A2B4007035].
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- Conjugation matrices
- Primary: 47A05
- Secondary: 47B35
- block Toeplitz operators
- complex symmetric operator matrices