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arXiv · 2103.01866

The numerical range of some periodic tridiagonal operators is the convex hull of the numerical ranges of two finite matrices

Benjamín A. Itzá-Ortiz·Rubén A. Martínez-Avendaño·Hiroshi Nakazato
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Abstract

In this paper we prove a conjecture stated by the first two authors establishing the closure of the numerical range of a certain class of $n+1$-periodic tridiagonal operators as the convex hull of the numerical ranges of two tridiagonal $(n+1) \times (n+1)$ matrices. Furthermore, when $n+1$ is odd, we show that the size of such matrices simplifies to $\frac{n}{2}+1$.

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Benjamín A. Itzá-Ortiz, Rubén A. Martínez-Avendaño, Hiroshi Nakazato. 2021-03-02. The numerical range of some periodic tridiagonal operators is the convex hull of the numerical ranges of two finite matrices. https://doi.org/10.1080/03081087.2021.1957760

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