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- W4384263664 abstract "We prove the first theorem on projections on general noncommutative $mathrm{L}^p$-spaces associated with non-type I von Neumann algebras where $1 leq p < infty$. This is the first progress on this topic since the seminal work of Arazy and Friedman [Memoirs AMS 1992] where the problem of the description of contractively complemented subspaces of noncommutative $mathrm{L}^p$-spaces is explicitly raised. We show that the range of a 2-positive contractive projection on an arbitrary noncommutative $mathrm{L}^p$-space is completely order isometrically isomorphic to some noncommutative $mathrm{L}^p$-space. This result is sharp and is even new for Schatten spaces $S^p$. Our approach relies on non-tracial Haagerup's noncommutative $mathrm{L}^p$-spaces in an essential way, even in the case of a projection acting on a Schatten space and is unrelated to the methods of Arazy and Friedman" @default.
- W4384263664 created "2023-07-14" @default.
- W4384263664 creator A5015704792 @default.
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- W4384263664 date "2019-12-03" @default.
- W4384263664 modified "2023-10-17" @default.
- W4384263664 title "2-positive contractive projections on noncommutative $mathrm{L}^p$-spaces" @default.
- W4384263664 doi "https://doi.org/10.48550/arxiv.1912.03128" @default.
- W4384263664 hasPublicationYear "2019" @default.
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