Abstract:
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.
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Received: 8 August 2000 / Accepted: 3 October 2000
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Davies, E. Spectral Theory of Pseudo-Ergodic Operators. Commun. Math. Phys. 216, 687–704 (2001). https://doi.org/10.1007/s002200000352
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DOI: https://doi.org/10.1007/s002200000352