Riesz and Szeg\"o type factorizations for noncommutative Hardy spaces

Let $\text{A}$ be a finite subdiagonal algebra in Arveson’s sense. Let $H^p(\text{A})$ be the associated noncommutative Hardy spaces, $0<p\le \text{8}$. We extend to the case of all positive indices most recent results about these spaces, which include notably the Riesz, Szeg"o and inner-outer type factorizations. One new tool of the paper is the contractivity of the underlying conditional expectation on $H^p(\text{A})$ for $p<1$.