On the Maximal Extensions of Monotone Operators, Criteria for Maximality, and the Sum Theorem

Host Institution:

RMIT

Title of Seminar:

On the Maximal Extensions of Monotone Operators, Criteria for Maximality, and the Sum Theorem

Speaker's Name:

Professor Andrew Eberhard

Speaker's Institution:

School of Mathematical and Geospatial Sciences, RMIT University

Time and Date:

Tuesday 22 October 2013, 3.00pm (AEDT)

Seminar Abstract:

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.

Seminar Convener:

This email address is being protected from spambots. You need JavaScript enabled to view it.

 

This email address is being protected from spambots. You need JavaScript enabled to view it.