Characterization of subdiagonal algebras on noncommutative Lorentz spaces

Let $(\mathcal{M}, \tau)$ be a finite von Neumann algebra, $\mathcal{A}$ be a tracial subalgebra of $\mathcal{M}$. We prove that $\mathcal{A}$ has $L^{p,q}$-factorization if and only if $\mathcal{A}$ is a subdiagonal algebra. We also obtain some characterizations of subdiagonal algebras.