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Dec 16, 2011 at 18:00 comment added Jon Bannon To actually answer the question, if the "right" definition is one for which double commutant and Kaplansky density hold, for example, then what you suggest works. Interestingly, it is mentioned in a book of Li that a (complex) operator algebra is the complexification of a real one if and only if the original algebra has a *-antiautomorphism. So not every von Neumann algebra is the complexification of a real one.
Dec 16, 2011 at 16:58 history edited Jon Bannon CC BY-SA 3.0
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Dec 16, 2011 at 16:53 history undeleted Jon Bannon
Dec 16, 2011 at 16:52 history deleted Jon Bannon
Dec 16, 2011 at 16:50 history answered Jon Bannon CC BY-SA 3.0