A pseudospectral mapping theorem

Lui, S.-H.

doi:10.1090/S0025-5718-03-01542-4

A pseudospectral mapping theorem
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Math. Comp. 72 (2003), 1841-1854 Request permission

Abstract:

The pseudospectrum has become an important quantity for analyzing stability of nonnormal systems. In this paper, we prove a mapping theorem for pseudospectra, extending an earlier result of Trefethen. Our result consists of two relations that are sharp and contains the spectral mapping theorem as a special case. Necessary and sufficient conditions for these relations to collapse to an equality are demonstrated. The theory is valid for bounded linear operators on Banach spaces. For normal matrices, a special version of the pseudospectral mapping theorem is also shown to be sharp. Some numerical examples illustrate the theory.

References

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