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), Universit\'e 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 (for every

$0< p<\infty$ ).

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