SMS scnews item created by Andrew Mathas at Tue 15 Oct 2013 1555
Expiry: 22 Oct 2013
Calendar1: 22 Oct 2013 1500-1600
CalLoc1: AGR Seminar
CalTitle1: AGR Seminar: On the Maximal Extensions of Monotone Operators, Criteria for Maximality, and the Sum Theorem
Auth: email@example.com in SMS-auth
On the Maximal Extensions of Monotone Operators, Criteria for Maximality, and the Sum Theorem
Prof Andrew Eberhard (School of Mathematical and Geospatial Sciences, RMIT University)
Within a nonzero, real Banach space we study the problem of characterising a maximal extension of a monotone operator in terms of minimality properties of representative functions that are bounded by the Penot and Fitzpatrick functions. We single out a property of the space of representative functions that enable a very compact treatment of maximality and pre-maximality issues. As this treatment does not assume reflexivity and we characterises this property the existence of a counter example has a number of consequences for the search for a suitable certificate for maximality in non-reflexive spaces. In particular one is lead to conjecture that some extra side condition to the usual CQ is inevitable. We go on to look at the simplest such condition which is boundedness of the domain of the monotone operator and obtain some positive results.
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