ROTUNDITY, THE CSRP, AND THE LAMBDA-PROPERTY IN BANACH-SPACES

Two open questions stemming from the lambda-property in Banach spaces are solved. The following are shown to be equivalent in a Banach space X: (a) X has the lambda-property; (b) every vector in the closed unit ball of X is expressible as a convex series of extreme points of the unit ball of X. Also, by exhibiting a class of nonrotund Orlicz spaces for which the lambda-function is identically 1 on the unit spheres, we answer negatively the question of whether the lambda-function characterizes rotund Banach spaces.