Reflexivity of convex subsets of L(H) and subspaces of \(l^ p\) (Q1173910)

Let \(H\) be a Hilbert space and \(S\) a convex subset of \(L(H)\). By the Hahn-Banach theorem, \(S\) is weak\(^{*}\) closed if and only if each \(u\not\in S\) can be separated fraom \(S\) be a nuclear operator via trace duality. In this paper, \(S\) is called \(k\)-reflexive if one can always pick an operator of rank \(\leq k\) to separate \(u\) from \(S\). The author studies \(k\)-reflexive convex sets; his results are a bit too technical to be reproduced here.