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

Wang, Jianhua

Acta Math. Sci., Ser. A, Chin. Ed. 26, No. 6, 840-846 (2006).

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)