A characterization of duality through section/projection correspondence in the finite dimensional setting

DOI10.1016/j.jfa.2011.08.007zbMath1258.52002OpenAlexW2052776242MaRDI QIDQ647618

Boaz A. Slomka, Alexander Segal, Vitali D. Milman

Publication date: 24 November 2011

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2011.08.007

zbMATH Keywords

dualitysectionpolar convex setsprojection correspondence

Mathematics Subject Classification ID

Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (4)

PROJECTIONS OF LOG-CONCAVE FUNCTIONS ⋮ Fixed points of polarity type operators ⋮ Dimension-raising homomorphisms between lattices of convex bodies ⋮ Order preserving and order reversing operators on the class of convex functions in Banach spaces

Cites Work

• The concept of duality for measure projections of convex bodies
• The endomorphisms of the lattice of closed convex cones
• A characterization of the duality mapping for convex bodies
• The endomorphisms of the lattice of norms in finite dimensions
• An elementary proof of the fundamental theorem of projective geometry
• The concept of duality in convex analysis, and the characterization of the Legendre transform
• On duality and endomorphisms of lattices of closed convex sets
• The Santaló point of a function, and a functional form of the Santaló inequality

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