Extremal properties of contraction semigroups on $c_o$

Details Extremal properties of contraction semigroups on $c_o$ Extremal properties of contraction semigroups on $c_o$

1994-12-19

arxiv.org/abs/math/9412216v1

Mathematics

Functional Analysis

Scientific paper

For any complex Banach space $X$, let $J$ denote the duality mapping of $X$. For any unit vector $x$ in $X$ and any ($C_0$) 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 $x^* \in J(x)$ such that $|\langle T(t) \, x,J(x)\rangle| \to 1 $ as $t \to \infty$, then there is a unit vector $y\in X$ 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.

Affiliated with

Also associated with

No associations

Rating

Extremal properties of contraction semigroups on $c_o$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Extremal properties of contraction semigroups on $c_o$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Extremal properties of contraction semigroups on $c_o$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-498825