TITLE: Is each element of factor(von Neumann algebra) a linear combination of projection?
QUESTION [2 upvotes]: Let $A$ be a factor von Neumann algebra. Then every element of $A$ can be writeen as a finite linear combination of projections in $A$. Is it right? I know a little about von Neumann algebra, thanks a lot to the one who tell me the answer or tell me where I can find the answer.
factor means $A\cap A'=\mathbb{C}I$.
Thanks a lot!

REPLY [3 votes]: The introduction to this article  by Kaftal et al mentions several references that address this question.
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