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Pré-Publication, Document De Travail Année : 2019

2-positive contractive projections on noncommutative Lp-spaces

2-positive contractive projections on noncommutative L p -spaces

Cédric Arhancet
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Résumé

We prove the first theorem on projections on general noncommutative L p-spaces associated with non-type I von Neumann algebras where 1 p < ∞. 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 L p-spaces is explicitly raised. We show that the range of a 2-positive contractive projection on an arbitrary noncommutative L p-space is completely order and completely isometrically isomorphic to some noncommutative 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 L pspaces 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.
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Dates et versions

hal-03992515 , version 1 (16-02-2023)

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Cédric Arhancet, Yves Raynaud. 2-positive contractive projections on noncommutative Lp-spaces. 2019. ⟨hal-03992515⟩
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