3 problems

Isometric transitivity conjecture. If $u\in V$ with $\lVert u\rVert=1$ is a norming order unit, then there exists a surjective linear isometry

Let $F$ be an ordered vector space with a filtration and let $\mathcal M_r$ denote the space of regular martingales. For a regular martingale $X=(x_n)$, write $|X|$ for its modulus…

Optimal-band bound conjecture. The optimal upper bound for the number of bands in $(X,K)$ is