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The stability of non-commutative $$L^p$$-spaces. (La stabilité des espaces $$L^p$$ non-commutatifs.) (French) Zbl 0914.46050
Summary: Let $$M$$ be a von Neumann algebra and $$R$$ the hyperfinite factor of type $$\text{II}_1$$. We show that if $$M$$ is not of type I then $$L^p(\mathbb{R})$$ is a 1-complemented subspace of $$L^p(M)$$ for all $$1\leq p<\infty$$. We also show that $$M$$ is of type I if and only if $$L^p(M)$$ is stable for all $$1\leq p<\infty$$.

MSC:
 46L51 Noncommutative measure and integration 46L53 Noncommutative probability and statistics 46L54 Free probability and free operator algebras 46L35 Classifications of $$C^*$$-algebras
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