Operating enlargements of monotone operators: new connections with convex functions

Benar Fux Svaiter | Burachik, Regina Sandra

Keywords: Banach spaces | Maximal monotone operators | enlargement of an operator | transportation formula | convex functions

Given a maximal monotone operator $T$ in a Banach space, a family of enlargements $\EE(T)$ of $T$ has been introduced by Svaiter. He also defined a sum and a positive scalar multiplication of enlargements. The first aim of this work is to further study the properties of these operations. Burachik and Svaiter studied a family of convex functions $\HH(T)$ which is in a one to one correspondence with $\EE(T)$. The second aim of this work is to prove that this bijection is in fact an isomorphism, for suitable operations in $\HH(T)$. Additionally, we prove that both spaces are convex with respect to these operations.

Anexos:

• xx10.ps