Abstract
We show that there exists a polyhedral Banach space X such that the closed unit ball of X is the closed convex hull of its extreme points. This solves a problem posed by J. Lindenstrauss in 1966.
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References
R. Durier and P. L. Papini, Polyhedral norms in an infinite-dimensional space, Rocky Mountain Journal of Mathematics 23 (1993), 863–875.
V. P. Fonf and L. Veselý, Infinite dimensional polyhedrality, Canadian Journal of Mathematics 56 (2004), 472–494.
V. P. Fonf, J. Lindenstrauss and R. R. Phelps, Infinite dimensional convexity, in Handbook of the Geometry of Banach Spaces, Vol. I, North-Holland, Amsterdam, 2001, pp. 599–670.
V. P. Fonf, J. Lindenstrauss and L. Veselý, Best approximation in polyhedral Banach spaces, Journal of Approximation Theory 163 (2011), 1748–1771.
V. Klee, Polyhedral sections of convex bodies, Acta Mathematica 103 (1960), 243–267.
J. Lindenstrauss, Notes on Klee’s paper: “Polyhedral sections of convex bodies”, Israel Journal of Mathematics 4 (1966), 235–242.
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Dedicated to Nicole and Fagiolino
Research supported in part by the Ministero dell’Istruzione, dell’Università e della Ricerca of Italy and by GNAMPA-INdAM.
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De Bernardi, C.A. Extreme points in polyhedral Banach spaces. Isr. J. Math. 220, 547–557 (2017). https://doi.org/10.1007/s11856-017-1539-2
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DOI: https://doi.org/10.1007/s11856-017-1539-2