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.
De Bernardi, C. A., Extreme points in polyhedral Banach spaces, <<ISRAEL JOURNAL OF MATHEMATICS>>, 2017; 220 (2): 547-557. [doi:10.1007/s11856-017-1539-2] [http://hdl.handle.net/10807/113750]
Extreme points in polyhedral Banach spaces
De Bernardi, Carlo Alberto
2017
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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