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| Volume 2, Number 3, September 2006, pp.425-445 | ||||||||
| Regina Sandra Burachik and Benar Fux Svatier | ||||||||
| Key words: | ||||||||
| Banach spaces, maximal monotone operators, enlargement of an operator, transportation formula,convex functions | ||||||||
| Mathematices Subject Classification: 47H05, 46B99, 47H17 | ||||||||
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| Abstract: | |||
| Given a maximal monotone operator T in a Banach space, a family of enlargements Ε(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 Η(T ) which is in a one to one correspondence with Ε(T ). The second aim of this work is to prove that this bijection is in fact an isomorphism, for suitable operations in Η(T ). Additionally, we prove that both spaces are convex with respect to these operations. | |||
| Operating enlargements of monotone operators: new connections with convex functions | ||