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Subdifferentials Whose Graphs Are Not Norm × Weak* Closed

Published online by Cambridge University Press:  20 November 2018

Jonathan Borwein ,
Simon Fitzpatrick  and
Roland Girgensohn
Jonathan Borwein
Affiliation:
Department of Mathematics Simon Fraser University Burnaby, British Columbia V5A 1S6, e-mail: jborwein@cecm.sfu.ca
Simon Fitzpatrick
Affiliation:
Department of Mathematics University of Western Australia Nedlands, Western Australia 6009 Australia, e-mail: fitzpatr@maths.uwa.edu.au
Roland Girgensohn
Affiliation:
GSF-Forschungszentrum Postfach 1129 85758 Neuherberg Germany, e-mail: girgen@gsf.de
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Abstract

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In this note we give examples of convex functions whose subdifferentials have unpleasant properties. Particularly, we exhibit a proper lower semicontinuous convex function on a separable Hilbert space such that the graph of its subdifferential is not closed in the product of the norm and bounded weak topologies. We also exhibit a set whose sequential normal cone is not norm closed.

Keywords

46N1047H05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 4 , 01 December 2003 , pp. 538 - 545
Copyright
Copyright © Canadian Mathematical Society 2003

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