The LMS JCM, (8) 17-45. Published 15 Feb 2005. First received 30 Sep 2004.


Spectral bounds using higher-order numerical ranges

E. B. Davies



Abstract:

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.



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