7 problems

Let $\mathcal{M}$ be a $\mathrm{JW}^*$-algebra equipped with a normal semifinite faithful trace $\tau$, and let $1{\leqslant} p<\infty$. Let $\mathrm{L}^p(\mathcal{M},\tau)$ denote…

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 reversible $\mathrm{JW}$-algebra equipped with a finite trace $\tau$, let $\mathcal{U}(A)$ be the von Neumann algebra generated by $A$, and extend $\tau$ to…

Let $A$ be a reversible $\mathrm{JW}$-algebra and let $A_{\mathbb{C}}=A+\mathrm{i}A$. Complex interpolation conjecture. For $1{\leqslant} p<\infty$, … This proposes an interpolatio…

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…

Let $A$ be a $\mathrm{JW}$-algebra with no direct summand isomorphic to the selfadjoint part of a von Neumann algebra, let $\mathcal{U}(A)$ be the von Neumann algebra generated by…

Let $A$ be a reversible $\mathrm{JW}$-algebra, let $\mathcal{U}(A)$ be the von Neumann algebra generated by $A$, let $A_{\mathbb{C}}=A+\mathrm{i}A$, and let $\varphi$ be a normal s…