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Relative modular theory for a weight


Author: Hideaki Izumi
Journal: Proc. Amer. Math. Soc. 127 (1999), 2703-2713
MSC (1991): Primary 46L10
DOI: https://doi.org/10.1090/S0002-9939-99-04840-6
Published electronically: April 15, 1999
MathSciNet review: 1600156
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Abstract: We consider the balanced weight $\chi$ of a semi-finite weight $\varphi$ and a (not necessarily faithful) normal positive functional $\psi$ on a von Neumann algebra $\mathcal M$, and discuss how the modular operator $\Delta _\chi$ and the modular conjugation $J_\chi$ are described under the identification of the standard Hilbert space $\mathcal{H}_\chi$ with $\mathcal{H}_\varphi \oplus p\mathcal{H}_\varphi\oplus p'\mathcal{H}_\varphi\oplus pp'\mathcal{H}_\varphi$, where $p$ is the support projection of $\psi$ and $p'=J_\varphi p J_\varphi\in\mathcal{M}'$.


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Additional Information

Hideaki Izumi
Email: h-izumi@math.tohoku.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-99-04840-6
Received by editor(s): March 31, 1997
Received by editor(s) in revised form: November 24, 1997
Published electronically: April 15, 1999
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society