9 problems

Let $A,B\in\mathcal S_n$, and let $\lVert\!\cdot\!\rVert$ be a unitarily invariant norm on matrices. The notation $|AB|$ denotes $(AB)^*AB$ raised to the power $1/2$, so…

Sharp arithmetic symmetric modulus conjecture. For every $X,Y\in\mathbb{M}_n$, there exist unitaries $U,V$ such that

Universal-constant Thompson domination. There should exist a universal constant $C$ such that, for every $X,Y\in\mathbb{M}_n$, there are unitaries $U,V$ satisfying

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…

Let $S\in\mathcal{M}_d(\mathbb{C})^+$ and $\mathbf{a}=(a_i)_{i\in\mathbb{I}_k}\in(\mathbb{R}^k_{>0})^\downarrow$. Define … For $\mathcal G\in\mathbb T_d(\mathbf a)$, write…

Norm inequality conjecture. For every unitarily invariant norm,

Let $A$ and $B$ be positive matrices, let $0\leq t\leq 1$, and let $|||\cdot|||$ be any unitarily invariant norm. Hayajneh–Kittaneh conjecture. One has … The conjecture concerns co…

Let $Z$ be an invertible matrix with polar decomposition $Z=U_p\sqrt{Z^*Z}$, where $U_p$ is its unitary polar factor, and let $\operatorname{Log}$ denote a matrix logarithm. Let…

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…