Let be a maximal subdiagonal algebra of semifinite von Neumann algebra . For , we define the noncommutative Hardy–Lorentz spaces , and give some properties of these spaces. We obtain that the Herglotz maps are bounded linear maps from into , and with this result we characterize the dual spaces of for . We also present the Hartman–Wintner spectral inclusion theorem of Toeplitz operators and Pisier’s interpolation theorem for this case.
"Noncommutative Hardy–Lorentz spaces associated with semifinite subdiagonal algebras." Banach J. Math. Anal. 10 (4) 703 - 726, October 2016. https://doi.org/10.1215/17358787-3649920