Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9495899 | Journal of Functional Analysis | 2005 | 21 Pages |
Abstract
We estimate the norm of the almost Mathieu operator Hθ,λ=Uθ+Uθ*+(λ/2)(Vθ+Vθ*), regarded as an element in the rotation C*-algebra Aθ=C*(Uθ,Vθunitaries:UθVθ=e2ÏiθVθUθ). In the process, we prove for every λâR and θâ[14,12] the inequality â¥Hθ,λâ¥â©½4+λ2-1-1tanÏθ1-1+cos24Ïθ2min{4,λ2}.This significantly improves the inequality â¥Hθ,2â¥â©½22, θâ[14,12], conjectured by Béguin, Valette and Zuk.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Florin P. Boca, Alexandru Zaharescu,