4 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 $A$ 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…

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