, Volume 216, Issue 3, pp 687-704

Spectral Theory of Pseudo-Ergodic Operators

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We define a class of pseudo-ergodic non-self-adjoint Schrödinger operators acting in spaces l 2(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 onl 2(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.

Received: 8 August 2000 / Accepted: 3 October 2000