3 problems

Lee's conjecture. For all $A,B\in M_n$,

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

Inflection-point conjecture. There exists an inflection point $\chi_n(\alpha)\in\bigl(H_{\text{\scriptsize \boldmath }v_n}(\mathrm{e}^{-n}),\ln n\bigr)$ such that…