2 problems

Let $1\leq p<\infty$, and let $T$ be the bilateral weighted shift on $\ell^p(\mathbb{Z})$ defined by … for a bounded positive weight sequence $(w_j)_{j\in\mathbb{Z}}$. Weak hypercy…

Let $T$ be an operator, let $T^*$ be its adjoint, and let $d4dc_1$ and $d4dc_2$ be subspaces. Assume that $T$ is $d4dc_1$-transitive and $T^*$ is $d4dc_2$-transitive. Orthogonal-co…