PreprintCC BY 4.0arXiv
Algebraic properties of Truncated Toeplitz + Truncated Hankel operators
Abstract
In this paper, we study the algebraic properties of 𝒮θ---the class of truncated Toeplitz plus truncated Hankel operators --- on the model space 𝒦θ. We also give a complete characterization of the intersection class of truncated Toeplitz and truncated Hankel operators under certain conditions. As applications, we describe the non-uniqueness of a decomposition T=A+B, show that self-adjoint operators admit self-adjoint decompositions, give a necessary and sufficient inclusion criterion for 𝒮θ when θ is a finite Blaschke product, and, from a first-order commutator characterization of 𝒮θ, describe the products of its elements and the operators commuting with Sθ+ Sθ*.
Related
- Matrix-Valued Truncated Toeplitz Operators: Properties and Applications
- Algebraic properties of Toeplitz operators on annulus and multiply connected domains
- Generalization of Toeplitz + Hankel operators in the polydisc
- The Skew Commutators of Toeplitz and Hankel operators in vector-valued Hardy Space
- Block Toeplitz Operators, Matrix Valued Truncated Toeplitz operators, and Conjugations
BibTeX
@misc{babbar2026algebraic,
title = {{Algebraic properties of Truncated Toeplitz $+$ Truncated Hankel operators}},
author = {Kritika Babbar and Satyabrata Majee and Amit Maji},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35897},
eprint = {2610.35897},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35897},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Algebraic properties of Truncated Toeplitz + Truncated Hankel operators
AU - Kritika Babbar
AU - Satyabrata Majee
AU - Amit Maji
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.35897
UR - https://arxiv.org/abs/2610.35897
AB - In this paper, we study the algebraic properties of 𝒮_θ---the class of truncated Toeplitz plus truncated Hankel operators --- on the model space 𝒦_θ. We also give a complete characterization of the intersection class of truncated Toeplitz and truncated Hankel operators under certain conditions. As applications, we describe the non-uniqueness of a decomposition T=A+B, show that self-adjoint operators admit self-adjoint decompositions, give a necessary and sufficient inclusion criterion for 𝒮_θ when θ is a finite Blaschke product, and, from a first-order commutator characterization of 𝒮_θ, describe the products of its elements and the operators commuting with S_θ+ S_θ^*.
ER -