4 problems

Let $(\mathcal{M}_k)_{k\geq 0}$ be the filtration and let $\mathcal{E}_k$ denote the corresponding conditional expectations; Theorem concerns the associated noncommutative martinga…

Let $\Phi$ be an Orlicz function satisfying the $\triangle_2$-condition, and let $x=(x_n)_{n\geq 1}$ be a noncommutative $L_1$-bounded martingale. For a martingale $u$, write…

Let $(\mathcal{M},\tau)$ be a noncommutative probability space, let $(\mathcal{M}_n)_{n\geq 1}$ be a weak-$*$ dense filtration of von Neumann subalgebras, and let…

Let $\Phi$ be the function appearing in Theorem (1), with lower and upper indices $p_{\Phi}$ and $q_{\Phi}$. The theorem currently assumes $q_{\Phi}<2$ together with $1<p_{\Phi}$.…