4 problems

Let $(\Phi,\Psi)$ be an admissible support function pair on a nest $\mathcal{E}$, and let $\mathcal M^0(\Phi,\Psi)$ be the bimodule constructed from this pair. Minimality conjectur…

Lie triple ring isomorphism conjecture. A mapping $\Phi\colon \operatorname{Alg}\mathcal{N}\longrightarrow \operatorname{Alg}\mathcal{M}$ is a Lie triple ring isomorphism, meaning…

Nonexistence conjecture. No epimorphism exists from an atomic nest algebra with all atoms finite rank onto either $B(\mathcal{H})$ or a continuous nest algebra.

Let $\mathcal{N}$ and $\mathcal{N}^\prime$ be nests on a Banach space $\mathbf{X}$, and let $\mathcal{A}\!\operatorname{lg}(\mathcal{N})$ and…