Subdifferentials Whose Graphs Are Not Norm$imes$Weak* Closed

[摘要] In this note we give examples of convex functions whosesubdifferentials have unpleasant properties. Particularly, weexhibit a proper lower semicontinuous convex function on aseparable Hilbert space such that the graph of its subdifferentialis not closed in the product of the norm and bounded weaktopologies. We also exhibit a set whose sequential normal cone isnot norm closed.

[学科分类] 数学（综合）