Let A be a type $I$ factor on a Hilbert space H. Let $\varphi$ be a semifinite normal weight on $A^{+}$ is it possible to say that then there exist Hilbert spaces $H_2 \subset H_1$ and an isomorphism of $H$ onto $H_2\otimes H_1$ such that A is isomorphic to $ \mathbb{C}_{H_2}\otimes B(H_1)$ ($\mathbb{C}_{H_2}$ denotes the scalars in $H_2$) and $$\varphi(T)=c\text{Tr}(P_{H_2}T) $$ for some scalar $c$.
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