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Journal of Operator Theory

Volume 48, Issue 1, Summer 2002  pp. 41-68.

On ultrapowers of non commutative $L_p$ spaces

Authors:  Yves Raynaud
Author institution: Equipe d'Analyse (CNRS), Université Paris 6, 4, place Jussieu, 75252 Paris Cedex 05, France

Summary:  It is well known that for every von Neumann Algebra $\rA$, every ultrapower of its predual $\rA_*$ is isometric to the predual of a von Neumann Algebra $\A$. We study the modular automorphism groups associated with states of $\A$ in terms of those for $\rA$. As an application we show that the ultrapower of the Haagerup $L_p(\rA)$ spaces are isometrically identifiable with the corresponding $L_p(\A)$ spaces (\textrm{for every } 0\lt p\lt \infty).

Keywords:  Ultrapowers, von Neumann algebras, Haagerup $L_p$ spaces

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