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

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

פרסום מחקרי: פרסום בכתב עתמאמרביקורת עמיתים

תקציר

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.

שפה מקוריתאנגלית
עמודים (מ-עד)3366-3389
מספר עמודים24
כתב עתJournal of Functional Analysis
כרך261
מספר גיליון11
מזהי עצם דיגיטלי (DOIs)
סטטוס פרסוםפורסם - 1 דצמ׳ 2011
פורסם באופן חיצוניכן

הערה ביבליוגרפית

Funding Information:
✩ The first and second named authors were partially supported by the ISF grant No. 387/09 and the third named author was partially supported by the ISF grant No. 865/07. * Corresponding author. Fax: +972 77 4220101. E-mail addresses: milman@post.tau.ac.il (V.D. Milman), segalale@gmail.com (A. Segal), boazslom@post.tau.ac.il, boazslomka@gmail.com (B.A. Slomka).

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