7 problems

Let $L(p,\theta,q)$ denote the spaces introduced in the preceding interpolation theorem, and let $[\,\ ]_\sigma$ denote the complex interpolation functor. For $0<p_0<1$ and…

Interpolation conjecture. The quasi-Banach spaces defined in the paper are complex interpolation spaces, completely isometrically, in the sense that

A Banach space $X$ is UMD if its Hilbert transform is bounded on $L^p(\mathbb{R};X)$ for all $p\in(1,\infty)$. It is intermediate UMD if it is $r$-intermediate UMD for some…

Let $X$ be an $r$-intermediate UMD space for some $r\in(2,\infty)$. Equivalently, there exist a UMD space $Y$ and a Hilbert space $H$ forming a compatible couple such that $X$ is i…

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…

Endpoint complex interpolation conjecture.