1993/04/01 by Denny H. Leung, Leung, Denny H.
Computer Science · Mathematics · #46B #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.math/9304206
openalex publication_date 1993/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 c0-saturated, i.e., each closed infinite dimensional subspace contains an isomorph of c0. In this paper, we show that the Orlicz sequence space hM is isomorphic to a polyhedral Banach space if limt→ 0M(Kt)/M(t) = ∞ for some K < ∞. We also construct an Orlicz sequence space hM which is c0-saturated, but which is not isomorphic to any polyhedral Banach space. This shows that being c0-saturated and having a separable dual are not sufficient for a Banach space to be isomorphic to a polyhedral Banach space.