Preprint A454/2006
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.