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: $%\def\rond{{\scriptstyle\circ}}$ $%\def\rA{{\hbox{\ronde a}}}$ $\def\rA{\mathfrak{A}}i$ 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 $\mathcal A$. We study the modular automorphism groups associated with states of $\mathcal A$ 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 $L_p(\mathcal A)$ spaces (\textrm{for every } 0\lt p\lt \infty).

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

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