Communications in Mathematical Physics

, Volume 216, Issue 3, pp 687–704

Spectral Theory of Pseudo-Ergodic Operators

  • E. B. Davies

DOI: 10.1007/s002200000352

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • E. B. Davies
    • 1
  1. 1.Department of Mathematics, King's College, Strand, London WC2R 2LS, UK.¶E-mail: