7 problems

Zhan's conjecture. For every $j=1,2,\ldots,n$, one should have

Complementary norm conjecture. For $1\leq p\leq\infty$,

Audenaert's in-betweenness conjecture. The weighted power means satisfy the in-betweenness property for every $p\geq 2$ and $0\leq t\leq 1$.

Let $A_1,\dots,A_m$ be positive definite matrices, let $w_1,\dots,w_m$ be weights, and let $0<t<1$. Define $P_t(w;A_1,\dots,A_m)$ as the unique positive definite solution of … wher…

Norm inequality conjecture. For every unitarily invariant norm,

Let $X$ and $Y$ be positive operators, and for $p\geq2$ define the weighted power mean $(tX^p+(1-t)Y^p)^{1/p}$ for $0\leq t\leq1$. Power-mean monotonicity conjecture. The function…

Reductive symmetry conjecture. All the symmetries of a quasi-mean obtained by recursive composition from $G_2$ are reductive symmetries, meaning that each can be formally proved us…