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On denseness of certain norms in Banach spaces. (English) Zbl 0866.46007

Summary: We give several results dealing with denseness of certain classes of norms with many vertex points. We prove that, in Banach spaces with the Mazur or the weak* Mazur intersection property, every ball (convex body) can be uniformly approximated by balls (convex bodies) being the closed convex hull of their strongly vertex points. We also prove hat given a countable set \(F\), every norm can be uniformly approximated by norms which are locally linear at each point of \(F\).

MSC:

46B20 Geometry and structure of normed linear spaces
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