- Title
- Subdifferentials whose graphs are not norm x weak* closed
- Creator
- Borwein, Jonathan; Fitzpatrick, Simon; Girgensohn, Roland
- Relation
- Canadian Mathematical Bulletin Vol. 46, Issue 4, p. 538-545
- Publisher Link
- http://dx.doi.org/10.4153/CMB-2003-051-5
- Publisher
- University of Toronto Press
- Resource Type
- journal article
- Date
- 2003
- Description
- 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.
- Subject
- monotone operators; convex functions; subdifferentials; weak topologies
- Identifier
- http://hdl.handle.net/1959.13/940729
- Identifier
- uon:13080
- Identifier
- ISSN:0008-4395
- Language
- eng
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