8 problems

Quantum KKL conjecture. There exists a universal constant $C>0$ such that for each $n\in\mathbb N$ and quantum Boolean function $T$,

In the classical setting, for a suitable nonnegative function $f$, the gradient of its square root satisfies an inequality controlled by the $L^1$ norm of its Hessian. In the non-c…

Let $B^s_{p,q}(\mathbb{R}^d_\theta)$ denote the inhomogeneous Besov space defined through the Littlewood–Paley decomposition, and let the quantum Besov spaces introduced by L. Lafl…

Let $H$ be a Hilbert space, let $L_1(H)$ denote the trace-class operators on $H$, and let $L_{1,cinfty}(H)$ denote the weak-$L_1$ space of compact operators $T$ whose singular valu…

The crossed-product factorization conjecture. For any Orlicz function $\psi$,

Sharpness conjecture. The right condition in Theorem (1) should be

Let $\|Y\|_{CL}$ and $\|Y\|_{NC}$ be the Carlen–Lieb and non-commutative norms, respectively, on matrices $Y\in {\cal M}_n\otimes {\cal M}_m$, with parameters $1<p\le2$ and $q\ge1$…

Let $\|Y\|_{CL}$ and $\|Y\|_{NC}$ denote the two non-commutative versions of the classical $L^q(L^p)$ norm on the matrix algebra ${\cal M}_n \otimes {\cal M}_m$, defined respective…