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Nov 26, 2016 at 18:25 comment added Hannes Thiel I see, that is a much more direct and more general argument. Very nice!
Nov 26, 2016 at 17:33 comment added Tomasz Kania That separable, infinite-dimensional C*-algebras are never complemented in their biduals (with any constant) follows also from an earlier result of Pfitzner that von Neumann algebras are Grothendieck spaces.
Nov 26, 2016 at 15:16 history answered Hannes Thiel CC BY-SA 3.0