On the Spectral Behaviour of a Non-self-adjoint Operator with Complex Potential
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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.
KeywordsComplex potential Non-self-adjoint Anderson model Numerical range Spectrum
Mathematics Subject Classifications (2000)47B80 47A12 60H25 65F15
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