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 מקורית | אנגלית |
|---|---|
| עמודים (מ-עד) | 3366-3389 |
| מספר עמודים | 24 |
| כתב עת | Journal of Functional Analysis |
| כרך | 261 |
| מספר גיליון | 11 |
| מזהי עצם דיגיטלי (DOIs) | |
| סטטוס פרסום | פורסם - 1 דצמ׳ 2011 |
| פורסם באופן חיצוני | כן |
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: [email protected] (V.D. Milman), [email protected] (A. Segal), [email protected], [email protected] (B.A. Slomka).