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Noncommutative $H^2$ spaces


Author: Michael Marsalli
Journal: Proc. Amer. Math. Soc. 125 (1997), 779-784
MSC (1991): Primary 47D15, 46L50
DOI: https://doi.org/10.1090/S0002-9939-97-03590-9
MathSciNet review: 1350954
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Abstract: Let $\mathcal M $ be a von Neumann algebra with a faithful, finite, normal tracial state $\tau $, and let $\mathcal A $ be a finite, maximal subdiagonal algebra of $\mathcal M $. Let $H^2$ be the closure of $\mathcal A $ in the noncommutative Lebesgue space $L^2(\mathcal M ,\tau )$. Then $H^2$ possesses several of the properties of the classical Hardy space on the circle, including a commutant lifting theorem, some results on Toeplitz operators, an $H^1$ factorization theorem, Nehari's Theorem, and harmonic conjugates which are $L^2$ bounded.


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Additional Information

Michael Marsalli
Affiliation: Department of Mathematics, Illinois State University, Normal, Illinois 61790-4520
Email: marsalli@math.ilstu.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03590-9
Received by editor(s): July 10, 1995
Received by editor(s) in revised form: July 27, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society

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