A re-examination of the Roberts example of a compact convex set without extreme points

DOI10.1007/BF01578905zbMath0448.46012MaRDI QIDQ1146848

Nigel J. Kalton, N. Tenney Peck

Publication date: 1980

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/163466

zbMATH Keywords

Radon-Nikodym propertycompact convex set without extreme pointsF-spaces in which the Krein-Milman theorem failsneedlepointOrlicz function space with trivial dual

Mathematics Subject Classification ID

Locally convex Fréchet spaces and (DF)-spaces (46A04) Convex sets in topological linear spaces; Choquet theory (46A55)

Related Items (10)

Compact convex sets and complex convexity ⋮ The fixed point property for weakly admissible compact convex sets: Searching for a solution to Schauder's conjecture ⋮ Obituary: Nigel John Kalton, 1946-2010 ⋮ Linear metric spaces and analytic sets ⋮ An F-space with trivial dual where the Krein-Milman theorem holds ⋮ The AR-property for Roberts’ example of a compact convex set with no extreme points Part 1: General result ⋮ The AR-property for Roberts’ example of a compact convex set with no extreme points Part 2: Application to the example ⋮ Fixed points for convex continuous mappings in topological vector spaces ⋮ Every Needle Point Space Contains a Compact Convex AR-Set with no Extreme Points ⋮ The Kakutani fixed point theorem for Roberts spaces

Cites Work

• Unnamed Item
• An F-space with trivial dual where the Krein-Milman theorem holds
• A compact convex set with no extreme points

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