Abstract
We prove that the closure of the numerical range of a \((n+1)\)-periodic and \((2m+1)\)-banded Toeplitz operator can be expressed as the closure of the convex hull of the uncountable union of numerical ranges of certain symbol matrices. In contrast to the periodic 3-banded (or tridiagonal) case, we show an example of a 2-periodic and 5-banded Toeplitz operator such that the closure of its numerical range is not equal to the numerical range of a single finite matrix.
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Communicated by Yiu-Tung Poon.
This paper is dedicated to Professor C.-K. Li.
The second author’s research is partially supported by the Asociación Mexicana de Cultura A.C.
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Itzá-Ortiz, B.A., Martínez-Avendaño, R.A. & Nakazato, H. The numerical range of periodic banded Toeplitz operators. Adv. Oper. Theory 9, 7 (2024). https://doi.org/10.1007/s43036-023-00304-7
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DOI: https://doi.org/10.1007/s43036-023-00304-7