Geodesic
Subdifferentials Whose Graphs Are Not Norm × Weak* Closed
Canadian mathematical bulletin, Tome 46 (2003) no. 4, pp. 538-545

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DOI

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.
DOI : 10.4153/CMB-2003-051-5
Mots-clés : 46N10, 47H05 
Borwein, Jonathan; Fitzpatrick, Simon; Girgensohn, Roland. Subdifferentials Whose Graphs Are Not Norm × Weak* Closed. Canadian mathematical bulletin, Tome 46 (2003) no. 4, pp. 538-545. doi: 10.4153/CMB-2003-051-5
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     author = {Borwein, Jonathan and Fitzpatrick, Simon and Girgensohn, Roland},
     title = {Subdifferentials {Whose} {Graphs} {Are} {Not} {Norm} {\texttimes} {Weak*} {Closed}},
     journal = {Canadian mathematical bulletin},
     pages = {538--545},
     year = {2003},
     volume = {46},
     number = {4},
     doi = {10.4153/CMB-2003-051-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-051-5/}
}
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