POLYHEDRAL NORMS IN AN INFINITE-DIMENSIONAL SPACE

In finite dimensional linear spaces, polyhedral norms have been widely studied. Many extensions of such notions to infinite-dimensional spaces are possible: in fact, several different definitions have been given, leading to different classes of spaces; the comparison among these classes has not been studied in detail. In the present paper we prove equivalences and inclusions among the classes considered in this context, and we indicate some counterexamples.