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Journal of Convex Analysis 17 (2010), No. 1, 309--320
Copyright Heldermann Verlag 2010

Non-Enlargeable Operators and Self-Cancelling Operators

Benar Fux Svaiter
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, RJ 22460-320, Brazil

The ε-enlargement of a maximal monotone operator is a construct similar to the Brĝndsted and Rockafellar ε-subdifferential enlargement of the subdifferential. Like the ε-subdifferential, the ε-enlargement of a maximal monotone operator has practical and theoretical applications.
Recently, R. S. Burachik and A. N. Iusem ["On non-enlargeable and fully enlargeable monotone operators", [J. Convex Analysis 13 (2006) 603--622] studied conditions under which a maximal monotone operator is non-enlargeable, that is, its ε-enlargement coincides with the operator. Burachik and Iusem studied these non-enlargeable operators in reflexive Banach spaces, assuming the interior of the domain of the operator to be nonempty. In the present work, we remove the assumption on the domain of non-enlargeable operators and also present partial results for the non-reflexive case.

Keywords: Maximal monotone operators, enlargements, Banach spaces.

MSC: 47H05, 49J52, 47N10

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