Kadets, V. M. Characterization of reflexive Banach spaces in terms of strongly exposed points of unbounded sets. (Russian) Zbl 0629.46013 Usp. Mat. Nauk 42, No. 3(255), 185-186 (1987). A convex cone K in a Banach space X is called normal if there is a constant \(C>0\) such that \(\| x\| \geq C\| y\|\) whenever, x,y,x-y\(\in K\). A convex set A in K is called a basis of K if for very \(x\in K\setminus \{0\}\) there is a \(t>0\) and a unique element \(y\in A\) such that \(x=ty\). An element \(a\in A\) is called strongly exposed if there is a functional \(f\in X'\) such that \(\lim_{\epsilon \to 0}diam \{x\in A|\) \(f(x)>f(a)-\epsilon \}=0.\) In this paper it is proved that in any nonreflexive Banach space there is a closed normal cone K with an unbounded basis A, consisting only of strongly exposed points. Reviewer: A.Torgašev Cited in 1 Review MSC: 46B20 Geometry and structure of normed linear spaces 46A55 Convex sets in topological linear spaces; Choquet theory 46A40 Ordered topological linear spaces, vector lattices 46B10 Duality and reflexivity in normed linear and Banach spaces Keywords:basis of a convex cone; normal cone; strongly exposed points PDFBibTeX XMLCite \textit{V. M. Kadets}, Usp. Mat. Nauk 42, No. 3(255), 185--186 (1987; Zbl 0629.46013)