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arXiv · 2609.04752

The Skew Commutators of Toeplitz and Hankel operators in vector-valued Hardy Space

Priyanka Aroda·Santanu Dey
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Abstract

In this article, we characterize when a Toeplitz operator and a Hankel operator on the vector-valued Hardy space are skew commutators of each other, and determine necessary and sufficient conditions under which their product is self-adjoint. These characterizations extend the results in \cite{LZD}. In addition, we completely classify the skew commutators of the unilateral shift $S$, its adjoint $S^*$ and $S\oplus S^*.$ We also characterize the class of bounded linear operators that have $S$, $S^*$ and $S\oplus S^*$ as skew-commutators.

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Priyanka Aroda, Santanu Dey. 2026-09-04. The Skew Commutators of Toeplitz and Hankel operators in vector-valued Hardy Space. https://arxiv.org/abs/2609.04752

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