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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)
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