An investigation is carried out of the compact convex sets X in an infinite-dimensional separable Hilbert space , for which the metric antiprojection from e to X has fixed cardinality n+1 ( arbitrary) for every e in a dense subset of . A similar study is performed in the case of the metric projection from e to X where X is a compact subset of .
* This work was supported by the CNR while the author was visiting the University of Milan.To a convex set in a Banach space we associate a convex function (the separating function), whose subdifferential provides useful information on the nature of the supporting and exposed points of the convex set. These points are shown to be also connected to the solutions of a minimization problem involving the separating function. We investigate some relevant properties of this function and of its conjugate...
Siano , sottoinsiemi convessi, chiusi e limitati di uno spazio normato , con le frontiere , . Dimostriamo che , dove è la metrica di Hausdorff tra sottoinsiemi chiusi di . Studiamo inoltre la continuità e la semicontinuità superiore ed inferiore di una multifunzione di tipo «frontiera».
Characterizations of extreme infinite symmetric stochastic matrices with respect to arbitrary non-negative vector r are given.
It is proved that there is a unique metrizable simplex whose extreme points are dense. This simplex is homogeneous in the sense that for every 2 affinely homeomorphic faces and there is an automorphism of which maps onto . Every metrizable simplex is affinely homeomorphic to a face of . The set of extreme points of is homeomorphic to the Hilbert space . The matrices which represent are characterized.