9 problems

Let $E$ be an ultra pseudo-normed $\widetilde{\mathbb K}$-module, let $E'$ denote its continuous linear functionals, and let $V$ be a submodule of $E$. For $\varphi\in V'$, the ext…

The setting is that of the paper's Ahlfors islands theorem, where $K$ is a non-archimedean field and $C_2$ is the lower-bound constant appearing in the hypothesis…

Let $K^{\lor}$ be the spherical completion of the underlying valued field $K$, let $V_K$ denote the relevant multiplicative value subgroup, and let $\sim$ denote the equivalence re…

Baroughan's conjecture. There exist a non-Archimedean Banach algebra $(B,\lVert *\rVert)$ over $\mathbb{Q}_p$ and an isometry

Non-Archimedean Zauner conjecture. For every $d\in\mathbb{N}$, there exist such vectors satisfying $\langle\tau_j,\tau_j\rangle=1$ for all $1\leq j\leq d^2$, with $S_\tau$ diagonal…

Non-Archimedean functional Zauner conjecture. For every $d\in\mathbb{N}$, there exist such vectors and functionals satisfying $f_j(\tau_j)=1$ for all $1\leq j\leq d^2$, with…

Let the hypotheses and notation be those of Theorem, in the general non-archimedean setting considered in the paper. Non-archimedean Broyden convergence conjecture. Broyden's metho…

Hyper-analyticity conjecture. This embedding yields hyper-analytic generalized smooth functions.

Hypercyclic and supercyclic criterion conjecture. Every hypercyclic, respectively supercyclic, linear operator on $c_0$ satisfies the Hypercyclic Criterion, respectively the Superc…