Nihonkai Mathematical Journal

The Radon-Nikodym theorem for non-commutative $L^{p}$-spaces

Hideaki Izumi

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Let $\cal M$ be a von Neumann algebra. We will show that for two normal semifinite faithful weights $\phi$, $\psi$ on $\cal M$, the corresponding non-commutative $L^p$-spaces $L^p({\cal M},\phi)$ and $L^p({\cal M},\psi)$ are isometrically isomorphic.

Article information

Nihonkai Math. J., Volume 19, Number 2 (2008), 137-150.

First available in Project Euclid: 18 March 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L51: Noncommutative measure and integration 46L52: Noncommutative function spaces 47L20: Operator ideals [See also 47B10]

Modular theory non-commutative integration Connes' Radon-Nikodym cocycle complex interpolation


Izumi, Hideaki. The Radon-Nikodym theorem for non-commutative $L^{p}$-spaces. Nihonkai Math. J. 19 (2008), no. 2, 137--150.

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