4 problems

Let $A,B\geq 0$. Let $f$ be a nonnegative and nondecreasing function on an interval $\mathcal{J}$ such that $\operatorname{spec}(A)\subseteq\mathcal{J}$. Reverse trace inequality.…

Compatibility conjecture. For $\alpha\in[2,\infty)$, the function $-\Psi_\alpha$ is $(\mathbb{H}^n_+,(2\alpha-1)/3)$-compatible with the domain $\mathbb{H}^n_+\times\mathbb{H}^n_+$…

Audenaert–Datta conjecture. If $1\leq p\leq2$, $-1\leq q<0$, and $s\geq1/(p+q)$, then this map is jointly convex. These conditions complement the necessary conditions stated in the…

Audenaert–Datta conjecture. If $1\leq p\leq2$ and $-1\leq q<0$, then this map is jointly convex. The conjecture specifies the parameter regime in which the trace functional underly…