## 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.## References

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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