Banach Journal of Mathematical Analysis

Noncommutative Hardy–Lorentz spaces associated with semifinite subdiagonal algebras

Yazhou Han

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Let A be a maximal subdiagonal algebra of semifinite von Neumann algebra M. For 0<p, we define the noncommutative Hardy–Lorentz spaces Hp,ω(A), and give some properties of these spaces. We obtain that the Herglotz maps are bounded linear maps from Λωp(M) into Λωp(M), and with this result we characterize the dual spaces of Hp,ω(A) for 1<p<. We also present the Hartman–Wintner spectral inclusion theorem of Toeplitz operators and Pisier’s interpolation theorem for this case.

Article information

Banach J. Math. Anal., Volume 10, Number 4 (2016), 703-726.

Received: 10 August 2015
Accepted: 25 December 2015
First available in Project Euclid: 31 August 2016

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Zentralblatt MATH identifier

Primary: 46L52: Noncommutative function spaces
Secondary: 46L51: Noncommutative measure and integration

subdiagonal algebras noncommutative Hardy–Lorentz spaces interpolation Toeplitz operators


Han, Yazhou. Noncommutative Hardy–Lorentz spaces associated with semifinite subdiagonal algebras. Banach J. Math. Anal. 10 (2016), no. 4, 703--726. doi:10.1215/17358787-3649920.

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