A characterization of duality through section/projection correspondence in the finite dimensional setting |
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Authors: | Vitali D Milman Boaz A Slomka |
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Institution: | School of Mathematical Science, Tel-Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel |
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Abstract: | In this paper, we show that the well-known duality operation in the context of convex bodies in Rn is completely characterized by its property of interchanging sections with projections. Our results are compared to results by Böröczky-Schneider and Artstein-Milman, who showed that in many cases, the property of order reversing is sufficient to determine a duality operation, up to obvious linear modifications. In fact, we provide another result that recovers a known characterization of duality by the property of order reversing, and up to a mild condition, also a characterization of duality by interchanging sections by projections. |
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Keywords: | Duality Polar convex sets Section-projection correspondence |
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