Let $M$ be a vN algebra(represented GNS space with respect to state) is in standard form, under which condition we can say a subalgebra $B$ of $M$ is also in standard form; My intuition is if there exists a conditional expectation state preserving from $M$ onto $B$, then $B$ will be in standard form(in GNS space of M)?? Is it true? Please comment thanks in advance.