A note on asymptotically isometric copies of $l^1$ and $c_0$

Hermann Pfitzner (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

Nonreflexive Banach spaces that are complemented in their bidual by an L-projection - like preduals of von Neumann algebras or the Hardy space $H^1$ - contain, roughly speaking, many copies of $l^1$ which are very close to isometric copies. Such $l^1$-copies are known to fail the fixed point property. Similar dual results hold for $c_0$.

Domaines: Analyse fonctionnelle [math.FA]

Hermann Pfitzner. A note on asymptotically isometric copies of $l^1$ and $c_0$. Proceedings of the American Mathematical Society, 2000, 129, pp.1367-1373. ⟨hal-00131643⟩