Order preserving and order preserving operators on the class of convex functions in Banach spaces

Seminar
Speaker
Dr. Daniel Reem, IMPA, Rio de Janeiro, Brasil
Date
23/01/2013 - 14:00Add to Calendar 2013-01-23 14:00:00 2013-01-23 14:00:00 Order preserving and order preserving 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 אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Abstract

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

Last Updated Date : 15/01/2013