7 problems

Randrianantoanina's conjecture. The range of every contractive projection on $X$ admits a block basis.

Let $H_p$ be the Hardy space, where $1\leqslant p<\infty$ and $p\ne 2$. A norm one projection on $H_p$ is a bounded projection $P:H_p\to H_p$ with norm one. Wojtaszczyk's conjectur…

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…

Let $0<p<1$, and let $P:H^p(\mathbb T)\to H^p(\mathbb T)$ be a contractive projection satisfying $P\mathbf 1=\mathbf 1$. Boundedness conjecture. The operator $P$ should automatical…

Let $E$ be a real JB$^*$-triple and let $P:E\to E$ be a contractive linear projection. Define the projected triple product on $P(E)$ by … for $a,b,c\in P(E)$. Projected-product con…