Abstract
In this paper, we focus on properties of the dilation of truncated Toeplitz operators on \(L^{2}\). In particular, we provide necessary and sufficient conditions for the dilation of truncated Toeplitz operators to be nonnegative and self-adjoint. Finally, we study the symbols \(\varphi \) and \(\psi \) when the dilation of truncated Toeplitz operators, \(S_{\varphi ,\psi }\) (defined below), is normal.
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Communicated by Victor Vinnikov.
Dedicated to the memory of Professor Takahiko Nakazi in deep sorrow.
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This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2016R1D1A1B03931937). The second author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2016R1A2B4007035).
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Ko, E., Lee, J.E. & Nakazi, T. On the Dilation of Truncated Toeplitz Operators II. Complex Anal. Oper. Theory 13, 3549–3568 (2019). https://doi.org/10.1007/s11785-019-00915-0
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DOI: https://doi.org/10.1007/s11785-019-00915-0