3 problems

Let $X$ be a strictly monotone Banach space with a $1$-unconditional basis, sufficiently different from a Hilbert space. Block-structure conjecture. Every norm-one projection on…

Let $X$ be a separable Banach space. A space is non-ergodic when it is not ergodic, and a Banach space is Hilbertian when it is isomorphic to a Hilbert space. Weak ergodicity conje…

Let $X$ be a Johnson space, meaning a separable Banach space with only countably many non-isomorphic subspaces. Weak Johnson conjecture. Every Johnson space has an unconditional ba…