3 problems

Uniform absorption conjecture. If $\boldsymbol{\mathcal{O}}$ is $w$-compact, then $\boldsymbol{\mathfrak{M}}$ is uniformly absorbing.

Let $M$ be a JBW$^*$-triple and let $M_*$ be its predual. For a functional $\varphi\in M_*$, let $\|\cdot\|_{\varphi}$ denote the associated seminorm. A bounded subset…

Mazur's conjecture. The space $X$ is reflexive if and only if every continuous linear functional on $X$ attains its maximum on the closed unit ball of $X$.