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Feb 23, 2021 at 11:23 comment added John It is true if you restrict $A$ and $B$ to be upwards-directed sets. This is essentially because of Kadison's characterisation of von Neumann algebras as being directed-complete C*-algebras (with a separating set of normal states). Hence, we can just take $z$ to be the supremum of $A$.
Jan 7, 2021 at 16:25 history became hot network question
Jan 7, 2021 at 9:47 vote accept Tomasz Kania
Jan 7, 2021 at 9:44 answer added Mateusz Wasilewski timeline score: 6
Jan 7, 2021 at 8:25 history asked Tomasz Kania CC BY-SA 4.0