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.
In which case weak compact coincides with weak operator topology compact？
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functional-analysis
operator-theory
operator-algebras
von-neumann-algebras