Journal of Convex Analysis 24 (2017), No. 1, 019--040
Copyright Heldermann Verlag 2017
On the Maximal Extensions of Monotone Operators and Criteria for Maximality
Andrew Eberhard
Mathematics Department, RMIT -- GPO Box 2476V, Melbourne, Vict. 3001, Australia
andrew.eberhard@ems.rmit.edu.au
Robert Wenczel
Mathematics Department, RMIT -- GPO Box 2476V, Melbourne, Vict. 3001, Australia
e01928@ems.rmit.edu.au
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 this space of representative functions that enable a very compact treatment of maximality and pre-maximality issues.
Keywords: Sum theorems, maximal extensions, monotone operators, representative functions.
MSC: 47H05, 46N10, 47H04, 49J53
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