Norm estimates of almost Mathieu operators

Details Norm estimates of almost Mathieu operators Norm estimates of almost Mathieu operators

2002-01-14

arxiv.org/abs/math-ph/0201028v2

Physics

Mathematical Physics

18 pages,3 figures

Scientific paper

We estimate the norm of the almost Mathieu operator $H_{\theta,\lambda}
=U+U^*+(\lambda /2)(V+V^*)$ in the rotation $C^*$-algebra $A_\theta =C^*(U,V
unitaries;UV=e^{2\pi i\theta} VU)$. In this process, we significantly improve
the inequality $\| H_\theta \| \leq 2\sqrt{2}$, $\theta \in [0.25,0.5]$,
conjectured by Beguin, Valette and Zuk.

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