2 problems

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…

Kadec–Pełczyński dichotomy conjecture. There exist a subsequence $(\phi_{\tau(n)})$ and a sequence of mutually orthogonal tripotents $(e_n)$ in $W$ such that