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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Noncommutative $H^2$ spaces
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by Michael Marsalli PDF
Proc. Amer. Math. Soc. 125 (1997), 779-784 Request permission

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
  • Received by editor(s): July 10, 1995
  • Received by editor(s) in revised form: July 27, 1995
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1997 American Mathematical Society
  • 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