PreprintCC BY 4.0arXiv
Matrix-Valued Truncated Toeplitz Operators: Properties and Applications
Abstract
In this paper, we present an application of matrix-valued truncated Toeplitz operators to the matrix version of the Nevanlinna-Pick interpolation problem. We then investigate the unitary part of a matrix-valued truncated Toeplitz operator induced by a contractive matrix-valued symbol. We further prove that, for a pure matrix-valued inner function, the corresponding model space is invariant under multiplication operator if and only if the symbol is constant. In addition, we give an algebraic proof of a characterization of the invertibility of matrix-valued asymmetric truncated Toeplitz operators using Toeplitz operators with 2 by 2 block matrix symbol. We also discuss the solvability of matrix-valued asymmetric truncated Toeplitz operators.
Related
- Block Toeplitz Operators, Matrix Valued Truncated Toeplitz operators, and Conjugations
- Algebraic properties of Truncated Toeplitz + Truncated Hankel operators
- Perturbations of Truncated Toeplitz operators
- Algebraic properties of Toeplitz operators on annulus and multiply connected domains
- Semialgebraic Dimension and Truncated Toeplitz Models for Complex Symmetric Matrices
BibTeX
@misc{khan2026matrixvalued,
title = {{Matrix-Valued Truncated Toeplitz Operators: Properties and Applications}},
author = {Rewayat Khan and Flavia Colonna},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15480},
eprint = {2609.15480},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15480},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Matrix-Valued Truncated Toeplitz Operators: Properties and Applications
AU - Rewayat Khan
AU - Flavia Colonna
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15480
UR - https://arxiv.org/abs/2609.15480
AB - In this paper, we present an application of matrix-valued truncated Toeplitz operators to the matrix version of the Nevanlinna-Pick interpolation problem. We then investigate the unitary part of a matrix-valued truncated Toeplitz operator induced by a contractive matrix-valued symbol. We further prove that, for a pure matrix-valued inner function, the corresponding model space is invariant under multiplication operator if and only if the symbol is constant. In addition, we give an algebraic proof of a characterization of the invertibility of matrix-valued asymmetric truncated Toeplitz operators using Toeplitz operators with 2 by 2 block matrix symbol. We also discuss the solvability of matrix-valued asymmetric truncated Toeplitz operators.
ER -