Remark on complex symmetric operator matrices

Abstract

In this paper, we study conjugation matrices and complex symmetric operator matrices. In particular, we investigate conditions for $2\times 2$ operator matrices to be conjugations or complex symmetric on $\mathcal{H}\oplus \mathcal{H}$. 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.

Keywords:

• Conjugation matrices
• complex symmetric operator matrices
• block Toeplitz operators

AMS Subject Classifications:

• Primary: 47A05
• Secondary: 47B35
• 47B15

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

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].