A characterization of the duality mapping for convex bodies

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Hidden structures in the class of convex functions and a new duality transform (2011, unknown): “The proof is complete. ut”
A characterization of the concept of duality (2007, background): “Assume we are given a transform T : Ξ(0)(R n) → Ξ(0)(R n) (defined on the whole domain Ξ(0)(R n)) satisfying (1) T T χK = χK (2) T (χK1χK2) = m̂ax(T χK1 , T χK2) Then, up to a symmetric linear transformation B ∈ GLn, T is the usual duality transform D taking the indicator function χK of a body K to…”
The concept of duality for measure projections of convex bodies (2008, methodology): “We note that our proof is different from the proofs of [6] and in particular we do not use their Theorem 9 quoted below but rather, we may use our reasoning to give an alternative proof of a similar theorem.”