The Eigenvalues of Tridiagonal Sign Matrices are Dense in the Spectra of Periodic Tridiagonal Sign Operators
Abstract
ChandlerWilde, 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 arXiv:
 arXiv:1412.1724
 Bibcode:
 2014arXiv1412.1724H
 Keywords:

 Mathematics  Spectral Theory;
 15B35;
 15A18 (Primary);
 47A10;
 47B36 (Secondary)
 EPrint:
 7 pages, 2 figures, minor changes (typos removed etc.)