Non-enlargeable operators and self-cancelling operators

Details Non-enlargeable operators and self-cancelling operators Non-enlargeable operators and self-cancelling operators

2008-07-07

arxiv.org/abs/0807.1090v3

Journal of Convex Analysis, 17 (2010), pp. 309--320

Mathematics

Functional Analysis

Submitted for publication in July 7, 2008

Scientific paper

The epsilon-enlargement of a maximal monotone operator is a construct similar to the Br{\o}ndsted and Rocakfellar epsilon-subdifferential enlargement of the subdifferential. Like the epsilon-subdifferential, the epsilon-enlargement of a maximal monotone operator has practical and theoretical applications. In a recent paper in Journal of Convex Analysis Burachik and Iusem studied conditions under which a maximal monotone operator is non-enlargeable, that is, its epsilon-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.

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