A pseudospectral mapping theorem |
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Authors: | S-H Lui |
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Institution: | Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2 |
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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. |
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Keywords: | Pseudospectra eigenvalues spectral mapping theorem |
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