Takesaki showed in section 6 of:
MR0303307 (46 #2445) Takesaki, Masamichi Conditional expectations in von Neumann algebras. J. Functional Analysis 9 (1972), 306–321. http://www.sciencedirect.com/science/article/pii/0022123672900043
that the following are equivalent for a von Neumann algebra M (not necessarily a factor):
- M is finite
- Every MASA in M admits a conditional expectation (i.e. norm one normal projection) onto it.
So
Edit: As Jon Bannon helpfully points out, the original question asked "when does a MASA admit a conditional expectation onto it", and so this answer in your case is only says "no", I think.not always" which isn't really a full answer!
