9 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…

Norm and completion conjecture. This definition defines a norm, and its completion is isometric to the Banach space $\mathrm{L}^p(\mathcal{M},\tau)$ defined in the paper.

Let $M$ be a finite von Neumann algebra and let $N$ be a semifinite von Neumann algebra. Suppose $1{\leqslant} p<\infty$ with $p\ne 2$, and let … be an isometry with a Yeadon facto…

Let $M$ be a finite von Neumann algebra and let $N$ be a semifinite von Neumann algebra. Suppose $1{\leqslant} p<\infty$ with $p\ne 2$, and let … be a not necessarily surjective is…

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 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…

The preceding result concerns Schatten classes and certain choices of the exponents. In the notation of the preceding inequality, let $u$, $v$, and $p$ be the parameters appearing…

USP conjecture for $L_p(\tau)$. For $2<p<\infty$, the space $L_p(\tau)$ is USP.