A Banach space X is called polyhedral if the unit ball of each one of its finite-dimensional (equivalently: two-dimensional [6]) subspaces is a polytope. Polyhedral spaces were studied by various authors; most of the structural results are due to V. Fonf. We refer the reader to the surveys [1], [2] for other definitions of polyhedrality, main properties and bibliography. In this paper we present a short alternative proof of the basic result on the structure of the unit ball of the polyhedral space (Theorem 1) and a related Theorem 2.
@article{urn:eudml:doc:38626,
title = {Boundary of polyhedral spaces: an alternative proof.},
journal = {Extracta Mathematicae},
volume = {15},
year = {2000},
pages = {213-217},
zbl = {0987.46019},
mrnumber = {MR1792990},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38626}
}
Vesely, Libor. Boundary of polyhedral spaces: an alternative proof.. Extracta Mathematicae, Tome 15 (2000) pp. 213-217. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38626/