Pathological maximal monotone operators

Host Institution:

The University of Newcastle

Title of Seminar:

Pathological maximal monotone operators

Speaker's Name:

Laureate Prof. Jon Borwein

Speaker's Institution:

CARMA, The University of Newcastle

Time and Date:

Thursday 5th Apr 2012, 9:30 am (AEST)

Seminar Abstract:

SIGMAOPT/OCANA Seminar 
http://carma.newcastle.edu.au/events/

In this paper, we construct maximally monotone operators that are not of Gossez's dense-type (D) in many nonreflexive spaces. Many of these operators also fail to possess the Brønsted-Rockafellar (BR) property. Using these operators, we show that the partial inf-convolution of two BC-functions will not always be a BC-function. This provides a negative answer to a challenging question posed by Stephen Simons. Among other consequences, we deduce that every Banach space which contains an isomorphic copy of the James space J or its dual J, or of c0 or its dual l1 admits a non type (D) operator.

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