Dual action of asymptotically isometric copies of $l_p (1\leq p < \infty)$ and $c_0$

P.N. Dowling and C.J. Lennard proved that if a Banach space contains an asymptotically isometric copy of $l_1$, then it fails the fixed point property. In this paper, necessary and sufficient conditions for a Banach space to contain an asymptotically isometric copy of $l_p(1\leq p <\infty)$ or $c_0$ are given by the dual action. In particular, it is shown that a Banach space contains an asymptotically isometric copy of $l_1$ if its dual space contains an isometric copy of $l_\infty$, and if a Banach space contains an asymptotically isometric copy of $c_0$, then its dual space contains an asymptotically isometric copy of $l_1$.