2 problems

Let $M$ be a von Neumann algebra with a faithful normal state $\varphi$, let $A$ be a $\mathrm{JW}$-algebra, and let $P\colon M\to M$ be a faithful normal positive unital projectio…

Let $A$ be a $\mathrm{JW}$-algebra, let $\mathcal{U}(A)$ be the von Neumann algebra generated by $A$, and let $\varphi$ be a faithful normal state on $\mathcal{U}(A)$. State-preser…