PreprintCC BY 4.0arXiv
The Skew Commutators of Toeplitz and Hankel operators in vector-valued Hardy Space
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⊕ S*. We also characterize the class of bounded linear operators that have S, S* and S⊕ S* as skew-commutators.
Related
- Generalization of Toeplitz + Hankel operators in the polydisc
- Algebraic properties of Truncated Toeplitz + Truncated Hankel operators
- Toeplitz and Hankel operators on Bergman spaces with doubling weights
- Block Toeplitz Operators, Matrix Valued Truncated Toeplitz operators, and Conjugations
- Hyponormal Toeplitz operators with operator valued normal symbols
BibTeX
@misc{aroda2026skew,
title = {{The Skew Commutators of Toeplitz and Hankel operators in vector-valued Hardy Space}},
author = {Priyanka Aroda and Santanu Dey},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04752},
eprint = {2609.04752},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04752},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Skew Commutators of Toeplitz and Hankel operators in vector-valued Hardy Space
AU - Priyanka Aroda
AU - Santanu Dey
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04752
UR - https://arxiv.org/abs/2609.04752
AB - 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⊕ S^*. We also characterize the class of bounded linear operators that have S, S^* and S⊕ S^* as skew-commutators.
ER -