Host Institution: 
University of South Australia 
Title of Seminar: 
On a sufficient condition for equality of two maximal monotone operators 
Speaker's Name: 
Assoc. Prof. Regina S. Burachik 
Speaker's Institution: 
University of South Australia 
Time and Date: 
Wednesday 28 April 2010 at 2:00 pm Sydney time (1:30 pm Adelaide time) 
Seminar Abstract: 
The first part of the talk is an introduction to enlargements of maximal monotone operators and some related theory. In the second part of the talk we establish minimal conditions under which two maximal monotone operators coincide. Our first result is inspired by an analogous result for subdifferentials of convex functions. In particular, we prove that two maximal monotone operators T, S which share the same convexlike domain D coincide whenever T(x) intersects S(x) for every x in D. We extend our result to the setting of enlargements of maximal monotone operators. More precisely, we prove that two operators coincide as long as the enlargements have nonempty intersection at each point of their common domain, the latter set assumed to be convexlike (a condition weaker than convexity) and open. We then use this result to obtain new facts for convex functions: we show that the difference of two convex functions whose subdifferentials have a common open convexlike domain is constant if and only if their epsilonsubdifferentials intersect at every point of that domain. The new results presented in the second part of the talk are joint work with Juan Enrique MartinezLegaz (Autonomous University of Barcelona) and Marco Rocco (Universita degli Studi di Bergamo).

Seminar Convenor: 
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