4 problems

Let $n\in\mathbb{N}$. For a closed, densely defined operator $T$, write $D(T^k)$ for the domain of its $k$-th power and $D[T^{*k}]$ for the domain of the $k$-th power of its adjoin…

Let $A$ be an unbounded self-adjoint operator on a Hilbert space. Unbounded commutator conjecture. There is always a bounded self-adjoint operator $B$ such that $AB-BA$ is unbounde…

Let $H$ be a complex Hilbert space. Let $A$ be an operator on $H$, densely defined and closed if necessary, and let $B\in B(H)$ be normal. Fuglede–Putnam conjecture. The inclusion…

Total form domain intersection conjecture. If dynamical decoupling works uniformly, then