On Haagerup noncommutative quasi Hp(A) spaces

Abstract

Let $M$ be a σ-finite von Neumann algebra, equipped with a normal faithful state φ, and let $A$ be a maximal subdiagonal subalgebra of $M$. We have proved that for $0<p<1$, $H^p\left(A\right)$ is independent of φ. Furthermore, in the case that $A$ is a type 1 subdiagonal subalgebra, we have obtained an interpolation theorem for $H^p\left(A\right)$ in the case where $0<\theta <1$, $0<p_0,p_1\le \infty$ and $p=\frac{1-\theta }{p_0}+\frac{\theta }{p_1}\ge 1$.