3 problems

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

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…