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Mathematical Physics, Analysis and Geometry

, Volume 10, Issue 1, pp 81–95 | Cite as

On the Spectral Behaviour of a Non-self-adjoint Operator with Complex Potential

  • Carmen Martínez Adame
Article

Abstract

We consider the non-self-adjoint Anderson operator with a complex potential as a pseudo-ergodic operator in one spatial dimension and use second order numerical ranges to obtain tight bounds on the spectrum of the operator. We also find estimates for the size of possible holes contained in the spectrum of such an operator.

Keywords

Complex potential Non-self-adjoint Anderson model Numerical range Spectrum 

Mathematics Subject Classifications (2000)

47B80 47A12 60H25 65F15 

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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Departamento de Matemáticas, Facultad de CienciasUNAMMéxico D.F.Mexico

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