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arXiv · 2308.12353

The numerical range of periodic banded Toeplitz operators

Benjamín A. Itzá-Ortiz·Rubén A. Martínez-Avendaño·Hiroshi Nakazato
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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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Benjamín A. Itzá-Ortiz, Rubén A. Martínez-Avendaño, Hiroshi Nakazato. 2023-08-23. The numerical range of periodic banded Toeplitz operators. https://doi.org/10.1007/s43036-023-00304-7

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