Extremal properties of contraction semigroups on c_o

1994/12/19 by Lin, P. K.
#46E #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.math/9412216

Abstract

For any complex Banach space X, let J denote the duality mapping of X. For any unit vector x in X and any (C₀) contraction semigroup (T_t)_t>0 on X, Baillon and Guerre-Delabriere proved that if X is a smooth reflexive Banach space and if there is x^* ∈ J(x) such that |⟨ T(t) x,J(x)⟩| → 1 as t → ∞, then there is a unit vector y∈ X which is an eigenvector of the generator A of (T_t)_t>0 associated with a purely imaginary eigenvalue. They asked whether this result is still true if X is replaced by c_o. In this article, we show the answer is negative.

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