报告题目 (Title)：ON ORDER PRESERVING AND ORDER REVERSING MAPPINGS（保序映射及逆序映射）
报告人 (Speaker)：程立新（厦门大学）
报告时间 (Time)：2024年5月9日(周四) 10:00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：席东盟、李晋、张德凯、吴加勇
主办部门：金沙威尼斯欢乐娱人城数学系
报告摘要：Suppose that X is a Banach space, Conv(X) is the cone of all continuous convex functions defined on X, and R^n is the n-dimensional Euclidean space. Artstein-Avidan and Milman showed the following elegant theorem in 2009: Every fully order reversing (resp. preserving) mapping Ƭ : Conv(R^n) → Conv(R^n) is essentially the Legendre transform (resp. the identity).
However, for a general Banach space X，the following questions remain unknown.
1. For what Banach spaces X，there is a fully order-reversing mapping Ƭ : Conv(X) → Conv(X)?
2. If Ƭ : Conv(X) → Conv(X) is a fully order-reversing mapping, whether T is essentially the Fenchel transform?
In this talk, we will give the two questions above affirmative answers.
