Duality for symmetric Hardy spaces of noncommutative martingales (Q1668430)

Let \(\mathcal{M}\) be a finite von Neumann algebra with a faithful normal finite trace \(\tau\), let \(\mathcal{A}\) be a subdiagonal subalgebra of \(\mathcal{M}\) and \(E\) a symmetric quasi-Banach space on \([0,1]\). The author introduces noncommutative Hardy spaces \(H_E(\mathcal{A})\) and generalizes to this setting various results obtained recently for noncommutative Hardy spaces \(H^p(\mathcal{A})\). In particular, he proves Szegő- and Riesz-type factorization theorems, investigates outer operators in the \(H_E(\mathcal{A})\) spaces, and shows that the Beurling invariant subspace theorem holds there as well (see [\textit{D. P. Blecher} and \textit{L. E. Labuschagne}, Trans. Am. Math. Soc. 360, No. 11, 6131--6147 (2008; Zbl 1160.46041); J. Oper. Theory 59, No. 1, 29--51 (2008; Zbl 1174.46030)] for \(H^p\) versions of the theorems).