3 problems

Let $X$ be a finite-dimensional Banach space, with $n=\dim X$. Finite-dimensional characterization conjecture. (a) If every one-dimensional subspace of $X$ can be represented as an…

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 rearrangement-invariant function space on $[0,1]$, so that $X$ contains the constant functions, and let $P$ be a contractive projection on $X$ satisfying…