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arXiv · 2207.06192

Characterizations of complex symmetric Toeplitz operators

Sudip Ranjan Bhuia·Deepak Pradhan·Jaydeb Sarkar
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Abstract

We present complete characterizations of Toeplitz operators that are complex symmetric. This follows as a by-product of characterizations of conjugations on Hilbert spaces. Notably, we prove that every conjugation admits a canonical factorization. As a consequence, we prove that a Toeplitz operator is complex symmetric if and only if the Toeplitz operator is $S$-Toeplitz for some unilateral shift $S$ and the transpose of the Toeplitz operator matrix is equal to the matrix of the Toeplitz operator corresponding to the basis of the unilateral shift $S$. Also, we characterize complex symmetric Toeplitz operators on the Hardy space over the open unit polydisc. Our results answer the well known open question about characterizations of complex symmetric Toeplitz operators.

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Sudip Ranjan Bhuia, Deepak Pradhan, Jaydeb Sarkar. 2022-07-26. Characterizations of complex symmetric Toeplitz operators. https://arxiv.org/abs/2207.06192

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