Projections from a von Neumann algebra onto a subalgebra.
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This paper is mainly devoted to the following question: Let $M,N$ be von~Neumann algebras with $Msubset N$, if there is a completely bounded projection $Pcolon N o M$, is there automatically a contractive projection $widetilde Pcolon N o M$? We give an affirmative answer with the only restriction that $M$ is assumed semi-finite.
