Purely imaginary eigenvalues of operator semigroups |
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Authors: | W M Ruess |
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Institution: | 1. Fachbereich Mathematik, Universit?t Essen, D-45117, Essen, Germany
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Abstract: | For aC
0-contraction semigroup (S(t))
t≥0 of bounded linear operators on a complex Banach spaceX, J. A. Goldstein and B. Nagy 6] have shown that, givenx∈X, S(t)x=e
iλt
x, t≥0, for some λ∈ℝ, provided lim
t→∞
|<S(t)x,x
*
>|=|<x,x
*
>| for allx
*∈X*. We present (a) an extension to the case of nonlinear nonexpansive mapsS(t), t≥0, and (b) various generalizations in the linear context. |
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Keywords: | |
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