Characterization of subdiagonal algebras on noncommutative Calderón–Lozanovskiĭ spaces

Abstract

Let $$\mathcal {M}$$ be a finite von Neumann algebra acting on a Hilbert space $$\mathcal {H}$$ with a faithful, normal, finite trace $$\tau$$ and let $$\mathcal {A}$$ be a tracial subalgebra of $$\mathcal {M}$$ . Let E be an $$\alpha$$ -convex symmetric quasi-Banach space on I for some $$0<\alpha <\infty$$ and let $$\varphi$$ be an Orlicz function. It is observed that $$\mathcal {A}$$ has $$E_\varphi$$ -factorization if and only if $$\mathcal {A}$$ is a subdiagonal algebra. Moreover, we present some characterizations of subdiagonal algebras.