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Norm estimates of almost Mathieu operators | Florin P. Boca
; Alexandru Zaharescu
; | Date: |
14 Dec 2001 | Subject: | Mathematical Physics; Operator Algebras; Spectral Theory MSC-class: 47B36;47A30;81Q10;46L60 | math-ph math.MP math.OA math.SP | Abstract: | We estimate the norm of the almost Mathieu operator $H_{ heta,lambda} =U+U^*+(lambda /2)(V+V^*)$ in the rotation $C^*$-algebra $A_ heta =C^*(U,V unitaries;UV=e^{2pi i heta} VU)$. In this process, we significantly improve the inequality $H_ heta leq 2sqrt{2}$, $ heta in [0.25,0.5]$, conjectured by Beguin, Valette and Zuk. | Source: | arXiv, math-ph/0201028 | Services: | Forum | Review | PDF | Favorites |
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