10 problems

Let $\operatorname{CL}_{\lVert\!\lVert\!\lVert\cdot\rVert\!\rVert\!\rVert}([0,\infty))$ denote the class of commutator-Lipschitz functions for the chosen unitarily invariant norm,…

Let $\widehat{\mathcal M}_+$ be the space of Fourier transforms of finite positive Borel measures on $\mathbb R$, and define … Let $f$ be a non-negative function that is operator m…

Let $\beta$ and $\alpha$ be parameters in the setting of Theorem $\text{alpha-beta-subopt}$, and let $C_{\alpha,\beta}$ and $C_{1-\alpha,1-\beta}$ denote constants independent of…

Let $A$ and $B$ be positive matrices, let $f$ be a function on $[0,infty)$ with $f(0)=0$, and let $|||\cdot|||$ be an arbitrary unitarily invariant norm. Ando-type conjecture. If…

The proper-subset conjecture. The class $GCV$ is a proper subset of $PMI$:

Extremality conjecture. The function $k_1^\mathrm{WYD}$ is an extreme point of $\mathcal{K}^+$. The function lies on the boundary of $\mathcal{K}^+$; the conjecture concerns whethe…

Let $A,B\geq 0$ be positive semidefinite matrices, let $f$ be an operator monotone function on $[0,\infty)$ with $f(0)=0$, and let $|||\cdot|||$ be a unitarily invariant norm on…

Gibilisco–Isola monotonicity conjecture. The determinant inequality

Monotonicity conjecture. For any $f,g\in{\cal F}_{op}^{\,r}$,

The N-volume inequality conjecture. For every $N\in{\mathbb N}$,