6 problems

Derivative contraction conjecture. If $c6$ induces a compact endomorphism of $D([0,1],M)$, then

Let $\mathbb A=(A_1,A_2,\dots,A_n)$ be a tuple of normal compact operators. For such a tuple, let $\sigma_p(\mathbb A)$ denote its projective point spectrum, and call the tuple com…

Majorization characterization conjecture. For every $A\in K(H)^+$,

Pairwise commutativity conjecture. The operators in ${\mathbb A}$ pairwise commute if and only if $\sigma_p({\mathbb A})$ is the union of countably many, locally finite, complex hy…

Let $A$ be a 1-matricial algebra, meaning an operator algebra with the 1-matricial structure described in the source, and let $\ell^2$ denote the Hilbert space of square-summable s…

Let $\mathcal{E}$ be a Banach space, let $\mathscr{C}\subset \mathcal{E}$ be a nonempty closed bounded convex set, and let $f\colon \mathscr{C}\to\mathscr{C}$ be a continuous map.…