Dual action of aymptotically isometric copies of lp(1<p<oo) and c0

Autores: H. Shutao Chen, Bor-Luh Lin
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 48, Fasc. 4-6, 1997, págs. 449-458
Idioma: inglés
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Resumen
- 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 $l_1$.