Dual action of asymptotically isometric copies of \(\ell_p\) \((1 \leq p < \infty)\) and \(c_0\)
P. N. Dowling and C. J. Lennard proved that if a Banach space contains an asymptotically isometric copy of \(\ell_1\), 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 \(\ell_p\) \((1\leq p<\infty)\) or \(c_0\) are given by the dual action. In particular, it is shown that a Banach space contains an asymptotically isometric copy of \(\ell_1\) if its dual space contains an isometric copy of \(\ell_\infty\), and if a Banach space contains an asymptotically isometric copy of \(c_0\), then its dual space contains an asymptotically isometric copy of \(\ell_1\).
scientific article; zbMATH DE number 1060656