On interpolation of noncommutative symmetric Hardy spaces (Q1683269)

\textit{W. B. Arveson} [Am. J. Math. 89, 578--642 (1967; Zbl 0183.42501)] introduced the notion of finite, maximal, subdiagonal algebras of a von Neumann algebra and extended the notion of weak\(^*\) Dirichlet algebras. In this paper, the authors study some properties of noncommutative analogues of symmetric Banach spaces. The first result is about the oncommutative analogue of pointwise product spaces. The authors give a new definition of the noncommutative symmetric Hardy spaces and obtain a Szegő-type factorization theorem and a first result about pointwise products for noncommutative symmetric Hardy spaces. Furthermore, the authors prove the noncommutative symmetric Hardy space version of a result of \textit{A. P. Calderón} [Stud. Math. 24, 113--190 (1964; Zbl 0204.13703)].