Extreme and Exposed Points of Spaces of Integral Polynomials

Abstract

We show that if E is a real Banach space such that E has the approximation property and such that 1 → n,s, E, then the set of extreme points of the unit ball of PI (nE) is equal to {±φn : φ ∈ E , φ = 1}. Under the additional assumption that E has a countable norming set, we see that the set of exposed points of the unit ball of PI (nE) is also equal to {±φn : φ ∈ E , φ = 1}.