if $E$ and $F$ are two projections in von Neumann algebra $M$, how to construct a unique central projection $P$ such that $PE \sim PF$?. The construction I am not getting?
2026-03-25 05:06:40.1774415200
Comparison theory of projections
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The idea of the proof is "take all central projections $P'$ such that $P'E\sim P'F$ and join them to obtain $P$". In more technical terms, this is achieved by considering a maximal family of pairwise orthogonal projections.