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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!

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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.