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Journal of Convex Analysis 13 (2006), No. 3, 883--887
Copyright Heldermann Verlag 2006

A New Convexity Property for Monotone Operators

Constantin Zalinescu
University "Al. I. Cuza", Faculty of Mathematics, Bd. Copou Nr. 11, 6600 Iasi, Romania
and: Inst. of Mathematics, Romanian Academy of Sciences, 700506 Iasi, Romania

It is well known that the interior of the domain of a maximal monotone operator is convex, and coincides with the core of its convex hull. In fact this is also true for the interior of the difference of the domains of two maximal monotone operators S and T. Recently, J. Borwein ["Maximal monotonicity via convex analysis, J. of Convex Analysis 13 (2006), this issue] used the condition that the origin is in the core of the convex hull of the difference of the graphs of S and -T in order to obtain that the origin is in the image of S+T. In this short note we show that gph(S) - gph(-T) has similar properties to dom(S) - dom(T).

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