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Spectral Bounds Using Higher-Order Numerical Ranges

Published online by Cambridge University Press:  01 February 2010

E. B. Davies
E. B. Davies
Affiliation:
Department of Mathematics, King's College, Strand London WC2R 2LS, United Kingdom, [email protected], http://www.mth.kcl.ac.uk/staff/eb_davies.html

Abstract

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This paper describes how to obtain bounds on the spectrum of a non-self-adjoint operator by means of what are referred to here as ‘its higher-order numerical ranges’. Proofs of some of their basic properties are given, as well as an explanation of how to compute them. Finally, they are used to obtain new spectral insights into the non-self-adjoint Anderson model in one and two space dimensions.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 8 , 2005 , pp. 17 - 45
Copyright
Copyright © London Mathematical Society 2005

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