6 problems

Let $E$ be $L^p( Omega, mu)$ for $1leq pleq infty$, or more generally a Banach lattice, and let $(Tt){tin(0,infty)}$ be a mean ergodic $C0$-semigroup on $E$. A **quasi-interior fix…

Let $\mathcal{H}$ be a Hilbert space and let $d\in\mathbb{N}$. Write $\mathcal{C}(\mathcal{H})^{d}_{\operatorname{comm}}$ for the set of $d$-tuples $\{S_i\}_{i=1}^d$ of commuting c…

Recall that for a bounded linear operator $T$, the essential spectrum is … For a $C_0$-semigroup $(T(t))_{t\geq 0}$ with generator $A$, the semigroup spectral mapping theorem would…

Decoupled Markov group conjecture. For every real number $M\geq 1$, there exists a real number $C=C(M)\geq0$ such that, for every $d\in\mathbb{N}$ and every matrix…

Referee's conjecture. The arguments and proof methods should also work for Dunford–Schwartz operators, not just for Koopman operators.

Weiss's conjecture. The resolvent condition should imply that $C$ is admissible for $A$; equivalently, the converse implication from the resolvent estimate to admissibility should…