Norm estimates of almost Mathieu operators
Florin P. Boca, Alexandru Zaharescu
Abstract
We estimate the norm of the almost Mathieu operator Hθ,λ =U+U*+(λ/2)(V+V*) in the rotation C*-algebra Aθ=C*(U,V unitaries;UV=e2πiθ VU). In this process, we significantly improve the inequality \| Hθ\| ≤ 22, θ∈ [0.25,0.5], conjectured by Beguin, Valette and Zuk.
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