Some isomorphically polyhedral Orlicz sequence spaces
Abstract
A Banach space is polyhedral if the unit ball of each of its finite dimensional subspaces is a polyhedron. It is known that a polyhedral Banach space has a separable dual and is $c_0$saturated, i.e., each closed infinite dimensional subspace contains an isomorph of $c_0$. In this paper, we show that the Orlicz sequence space $h_M$ is isomorphic to a polyhedral Banach space if $\lim_{t\to 0}M(Kt)/M(t) = \infty$ for some $K < \infty$. We also construct an Orlicz sequence space $h_M$ which is $c_0$saturated, but which is not isomorphic to any polyhedral Banach space. This shows that being $c_0$saturated and having a separable dual are not sufficient for a Banach space to be isomorphic to a polyhedral Banach space.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 1993
 arXiv:
 arXiv:math/9304206
 Bibcode:
 1993math......4206L
 Keywords:

 Mathematics  Functional Analysis;
 46B