Applications sous-linéaires à valeurs dans un espace de fonction continues. (Sublinear mappings with values in a space of continuous functions) (Q1086790)

The authors give several conditions based upon the condition that a sublinear function f from the Banach space X into C(T) (T-compact Hausdorff) is iso lower semicontinuous which are sufficient to imply that f is approximable from below at each x in its domain by continuous affine maps from X into C(T). Examples are given to show that certain features of the sufficient conditions are necessary.