In this paper, we investigate the complex symmetric structure of Toeplitz operators $T_\phi$ on the Hardy space over the bidisk. We first characterize the weighted composition operators, $W_{u,v}$ which are $\mathcal{J}$-symmetric and unitary. As a consequence, we characterize conjugations of the form $A_{u,v}$. In addition, a class of conjugations of the form $C_{\lambda, a}$ is introduced. We show that the class of conjugations $C_{\lambda, a}$ coincides with the class of conjugations $A_{u,v}$; we then characterize the complex symmetry of the Toeplitz operators $T_\phi$ with respect to the conjugation $C_{\lambda, a}$.
Maofa Wang
,
Qi Wu
,
Kaikai Han
. COMPLEX SYMMETRY OF TOEPLITZ OPERATORS OVER THE BIDISK∗[J]. Acta mathematica scientia, Series B, 2023
, 43(4)
: 1537
-1546
.
DOI: 10.1007/s10473-023-0405-z
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