5 problems

Let $U^n$ be the unit polydisk, let $p,q\in(0,1)$, and let $\phi$ be a holomorphic self-map of $U^n$. Write $C_\phi f=f\circ\phi$ for the composition operator, and let…

Nonexistence conjecture. There are no isometric weighted composition operators

Let $g$ belong to the Bloch space $4\mathcal{B}4$. For each nonzero $\lambda\in\mathbb{C}$, define … Assume that every $w_\lambda$ satisfies the $B_\infty$ condition. Closure chara…

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…

Let $D$ be a bounded homogeneous domain, let $H(D)$ denote the holomorphic functions on $D$, and let $M_\psi$ be the multiplication operator induced by $\psi\in H(D)$ on the Bloch…