Subdifferentials Whose Graphs Are Not Norm × Weak* Closed
Jonathan Michael Borwein, Simon Fitzpatrick, Roland Girgensohn · Canadian Mathematical Bulletin · 2003
Abstract 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.