Journal of Operator Theory

Volume 56, Issue 1, Summer 2006 pp. 59-88.

Spectral estimates for the one-dimensional non-self-adjoint Anderson Model

Authors: Carmen Martinez
Author institution: Departamento de Matem\'aticas, Facultad de Ciencias, U.N.A.M., Mexico City, 04510, Mexico

Summary: We obtain bounds on the spectrum of the non-self-adjoint Anderson operator in one dimension by using higher order numerical ranges and are able to determine the spectrum completely in many cases. We also develop further some previously existing methods that allow us to prove that certain curves and regions are contained in the spectrum and provide numerical examples that suggest that these curves contained in the infinite volume spectrum have a strong bearing over the finite volume cases.

Keywords: Anderson model, non-self-adjoint operator, spectrum, numerical range, ergodic operator

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