Monotone operators without enlargements
Date
2013
Authors
Borwein, J.M.
Burachik, R.S.
Yao, L.
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Bailey, D.H.
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Book chapter
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Source details - Title: Computational and analytical mathematics, 2013 / Bailey, D.H. (ed./s), vol.50, Ch.5, pp.79-103
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Abstract
Enlargements have proven to be useful tools for studying maximally monotone mappings. It is therefore natural to ask in which cases the enlargement does not change the original mapping. Svaiter has recently characterized non-enlargeable operators in reflexive Banach spaces and has also given some partial results in the nonreflexive case. In the present paper, we provide another characterization of non-enlargeable operators in nonreflexive Banach spaces under a closedness assumption on the graph. Furthermore, and still for general Banach spaces, we present a new proof of the maximality of the sum of two maximally monotone linear relations. We also present a new proof of the maximality of the sum of a maximally monotone linear relation and a normal cone operator when the domain of the linear relation intersects the interior of the domain of the normal cone.
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Copyright 2013 Springer Science+Business Media