# The eigenvalues of tridiagonal sign matrices are dense in the spectra of periodic tridiagonal sign operators

Hagger, R. (2015) The eigenvalues of tridiagonal sign matrices are dense in the spectra of periodic tridiagonal sign operators. Journal of Functional Analysis, 269 (5). pp. 1563-1570. ISSN 0022-1236

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To link to this item DOI: 10.1016/j.jfa.2015.01.019

## Abstract/Summary

Chandler-Wilde, Chonchaiya and Lindner conjectured that the set of eigenvalues of finite tridiagonal sign matrices ($\pm 1$ on the first sub- and superdiagonal, $0$ everywhere else) is dense in the set of spectra of periodic tridiagonal sign operators on $\ell^2(\mathbb{Z})$. We give a simple proof of this conjecture. As a consequence we get that the set of eigenvalues of tridiagonal sign matrices is dense in the unit disk. In fact, a recent paper further improves this result, showing that this set of eigenvalues is dense in an even larger set.

Item Type: Article Yes Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics 84019 Elsevier