Spectral Theory of Pseudo-Ergodic Operators
- Cite this article as:
- Davies, E. Commun. Math. Phys. (2001) 216: 687. doi:10.1007/s002200000352
We define a class of pseudo-ergodic non-self-adjoint Schrödinger operators acting in spaces l2(X) and prove some general theorems about their spectral properties. We then apply these to study the spectrum of a non-self-adjoint Anderson model acting onl2(Z), and find the precise condition for 0 to lie in the spectrum of the operator. We also introduce the notion of localized spectrum for such operators.