The metric projections in nonreflexive Banach spaces.(Chinese. English summary)Zbl 1116.46301

Summary: The author gives a representation of the metric projection $$P_H$$ on a class of hyperplanes in a nonreflexive Banach space and proves that if $$X$$ is (weakly) nearly strictly convex, then $$P_H$$ is (norm-weakly) norm-norm upper semicontinuous. For a dual Banach space $$X^*$$, some results on continuity of the metric projections on the weak* closed subsets are derived.

MSC:

 46B20 Geometry and structure of normed linear spaces 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)