Abelian subalgebras of von Neumann algebras Is it true that one always have faithful normal conditional expectation from von Neumann algebra $M$ to any abelian subalgebra $A\subset M$? Does it hold for some special class of von Neumann algebras?

By a theorem of Takesaki (Section 6 in Conditional Expectations in von Neumann Algebras) there exists a normal conditional expectation onto every maximally abelian subalgebra of $M$ if and only if $M$ is finite. So finiteness of $M$ is necessary.
If $M$ is finite, there is a faithful normal conditional expectation onto every von Neumann subalgebra $N$. This can be constructed as the restriction of the orthogonal projection $L^2(M,\tau)\to L^2(N,\tau)$, where $\tau$ is a faithful normal tracial state on $M$.
