4 problems

Let $A$ be an infinite-dimensional unital Banach algebra. Dales–Zelazko conjecture. Then $A$ has a maximal left ideal which is not finitely generated. The conjecture concerns the e…

Non-diagonal-boundedness conjecture. If $\omega$ is not diagonally bounded, then $L^1(G,\omega)$ is not pseudo-amenable.

The 2-weak amenability conjecture. If this condition holds for every $t\in G$, then $L^1(G,\omega)$ is $2$-weakly amenable.

Let $G$ be a locally compact abelian group and let $L^1_\omega(G)$ be its Beurling algebra, where $\omega$ is a weight. Assume that … for every $t\in G$. Dales–Lau conjecture. Unde…