Bar-Ilan University                                               
ANALYSIS SEMINAR                                                  

Speaker: Dr. Daniel Reem                                          
IMPA,  Rio de Janeiro, Brasil                                     
Date: Wednesday, January 23, 2013                                 
Time: 14:00                                                       
Place: 2nd floor Colloquium Room, Building 216                    
Title:  Order preserving and order reversing operators on the     
       class of convex functions in Banach spaces                 
Recently S. Artstein-Avidan and V. Milman have developed an       
abstract duality theory and proved the following remarkable       
result: up to linear terms, the only fully order preserving       
operator (namely, an invertible operator whose inverse also       
preserves the pointwise order between functions) acting           
on the class of lower semicontinuous proper convex functions      
defined on R^n is the identity operator, and the only fully       
order reversing operator acting on the same set is the            
Fenchel conjugation (Legendre transform). We establish            
a suitable extension of their result to infinite dimensional      
Banach spaces.                                                    
This is a joint work with Alfredo N. Iusem and Benar F. Svaiter   
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <> 
Announcement from: Elijah Liflyand   <>