Norm estimates of almost Mathieu operators

Florin P. Boca, Alexandru Zaharescu

We estimate the norm of the almost Mathieu operator $H_{\theta ,\lambda }=U+U^{\ast }+(\lambda /2)(V+V^{\ast })$ in the rotation $C^{\ast }$-algebra $A_{\theta }=C^{\ast }(U,Vunitaries;UV=e^{2\pi i\theta }VU)$. In this process, we signifi…