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

Abstract

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.