7 problems

Let $X$ be compact, let $E$ be a Banach space continuously embedded in $(C(X),\tau_p)$, and let $C_{w,\varphi}:E\to E$ be an isometric weighted composition operator. Non-supercycli…

Higher-dimensional affine-symbol conjecture. Every bounded weighted composition operator with nonvanishing weight has affine symbol. This would extend the affine-symbol result from…

Converse characterization conjecture. The set $\{\lvert\lambda\rvert: \lambda \mathds{T} \subset \sigma_{usf}(T)\}$ is at most countable and its only accumulation point, if any, is…

Nonexistence conjecture. There are no isometric weighted composition operators

Let $u,v\in H(\mathbb{B})$ and let $\varphi,\psi$ be holomorphic self-maps of $\mathbb{B}$. For $k\in\mathbb{N}\cup\\{0\\}$ and $\xi\in\partial\mathbb{B}$, write…

Non-normality conjecture. No non-normal quasinormal weighted composition operators exist in this case; equivalently, every quasinormal weighted composition operator with weight not…

Let $X$ be a Banach lattice with Stonean compact $K$, let $Y$ be the subspace and $T$ the weighted composition operator from Proposition 1, and let $S$ be the corresponding weighte…