Open Access
October 2016 Noncommutative Hardy–Lorentz spaces associated with semifinite subdiagonal algebras
Yazhou Han
Banach J. Math. Anal. 10(4): 703-726 (October 2016). DOI: 10.1215/17358787-3649920


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.


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Yazhou Han. "Noncommutative Hardy–Lorentz spaces associated with semifinite subdiagonal algebras." Banach J. Math. Anal. 10 (4) 703 - 726, October 2016.


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

zbMATH: 1367.46052
MathSciNet: MR3543908
Digital Object Identifier: 10.1215/17358787-3649920

Primary: 46L52
Secondary: 46L51

Keywords: interpolation , noncommutative Hardy–Lorentz spaces , subdiagonal algebras , Toeplitz operators

Rights: Copyright © 2016 Tusi Mathematical Research Group

Vol.10 • No. 4 • October 2016
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