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Dmitri Pavlov
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Can a finite von Neumann algebra be strongly morita equivalent to a properly infinite von neumann algebra?

Can a finite (by finite I mean when the projection $1$ is finite) von Neumann algebra be strongly morita equivalent to a properly infinite von Neumann algebra?

(Strong morita equivalence is the same as Morita equivalence as a ring for $C^*$-algebras according to the theorem on page 253 of http://www.sciencedirect.com/science/article/pii/0022404982901098, see remark 1.5 for definition of strong Morita equivalence)

Louis A
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