TY - JOUR
T1 - Norm estimates of almost Mathieu operators
AU - Boca, Florin P.
AU - Zaharescu, Alexandru
PY - 2005/3/1
Y1 - 2005/3/1
N2 - 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, Vθ unitaries : Uθ Vθ = e2πiθVθUθ). In the process, we prove for every λ ∈ ℝ and θ ∈ [1/4, 1/2] the inequality A formula is presented. This significantly improves the inequality ∥Hθ,2∥ ≤ 2 2, θ ∈ [1/4, 1/2], conjectured by Béguin, Valette and Zuk.
AB - 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, Vθ unitaries : Uθ Vθ = e2πiθVθUθ). In the process, we prove for every λ ∈ ℝ and θ ∈ [1/4, 1/2] the inequality A formula is presented. This significantly improves the inequality ∥Hθ,2∥ ≤ 2 2, θ ∈ [1/4, 1/2], conjectured by Béguin, Valette and Zuk.
KW - Almost Mathieu operators
KW - Norms
KW - Rotation C-algebras
UR - http://www.scopus.com/inward/record.url?scp=12444266896&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=12444266896&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2004.09.013
DO - 10.1016/j.jfa.2004.09.013
M3 - Article
AN - SCOPUS:12444266896
SN - 0022-1236
VL - 220
SP - 76
EP - 96
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -