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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Noncommutative $H^2$ spaces

Author: Michael Marsalli
Journal: Proc. Amer. Math. Soc. 125 (1997), 779-784
MSC (1991): Primary 47D15, 46L50
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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Michael Marsalli
Affiliation: Department of Mathematics, Illinois State University, Normal, Illinois 61790-4520

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