I have been reading a paper in which the authors used Ryll-Nardezwiski fixed point theorem. However, they didn't show the set is weakly compact. So, I would like to ask here, for a WOT compact convex subset of a von Neumann algebra, what conditions we need in order to ensure this subset is weakly compact? e.g., separable vNa etc.
2026-03-28 01:12:52.1774660372
In which case weak compact coincides with weak operator topology compact？
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