Exposed points of the unit balls of the spaces P (²l _p²) (p = l, 2, ∞)

Ryan and Turett showed that for finite-dimensional space E, the set of exposed points and the set of extreme points of the closed unit ball of Ê_π⁽ⁿ⁾ coincide, where Ê_π ⁽ⁿ⁾ is the completed n-fold symmetric tensor product of E with the projective s-tensor norm. In this note we show that a similar result is not true for the dual space P(ⁿE) and classify the exposed points of the unit balls of the spaces P (²l_p²) for p= l, 2, ∞.