A spectral radius theorem for matrix seminorms |
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| Authors: | John A Feroe |
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| Institution: | Department of Mathematics Vassar College Poughkeepsie, New York 12601 USA |
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| Abstract: | A matrix seminorm ∥·∥ is called supspectral if it satisfies the condition that the spectral radius of a square matrix A is lim sup ∥An∥1/n as n→∞. This property is shown to be equivalent to each of two conditions on ∥·∥, one characterizing behavior on idempotent A, and the other characterizing behavior on non-nilpotent A. Examples of supspectral seminorms are provided. |
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