Banach Journal of Mathematical Analysis

Noncommutative Hardy–Lorentz spaces associated with semifinite subdiagonal algebras

Yazhou Han

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1472657853

Digital Object Identifier
doi:10.1215/17358787-3649920

Mathematical Reviews number (MathSciNet)
MR3543908

Zentralblatt MATH identifier
1367.46052

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

Keywords
subdiagonal algebras noncommutative Hardy–Lorentz spaces interpolation Toeplitz operators

Citation

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. https://projecteuclid.org/euclid.bjma/1472657853


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