Let A be closed convex set and let C be the intersection of the closed unit ball (of the dual space) with the barrier cone of A.
If the support function of A is bounded on C, then C is closed since the support function is lower semicontinuous. Is the converse true? I don't have hopes that it is so in an infinite-dimensional space, but is it in R^n?
If not, what extra conditions on A ensure the boundedness of the support function on C?
Many thanks!
For symmetric A (i.e. such that A = - A) this is true in every Banach space, but I don't know if this particular case is interesting for you.
Thank you, unfortunately the symmetric case doesn't help me much.
Btw, the first paper I ever printed was yours.
Very nice example!
I'll try to pay you back by reading your papers with Cascales and Rodríguez, which have been on my table for quite some time.
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