## Annals of Functional Analysis

### The Hankel operators and noncommutative BMO spaces

Cheng Yan

#### Abstract

Let $\mathcal{M}$ be a von Neumann algebra with a faithful normal semifinite trace $\tau$. The noncommutative Hardy space $H^{p}(\mathcal{M})$ associates with $\mathcal{A}$, which is a subdiagonal algebra of $\mathcal{M}$. We define the Hankel operator $H_{t}$ on $H^{p}(\mathcal{M})$, and we obtain that the norm $\Vert H_{t}\Vert$ is equal to $d(t;\mathcal{A})$ and is also the equivalent of the $\operatorname{BMO}(\mathcal{M}^{\mathrm{sa}})$ norm of $t$ for every $t\in\mathcal{M}$, where $\mathcal{M}^{\mathrm{sa}}$ are the self-adjoint operators in $\mathcal{M}$.

#### Article information

Source
Ann. Funct. Anal., Volume 7, Number 3 (2016), 402-410.

Dates
Accepted: 4 December 2015
First available in Project Euclid: 17 June 2016

https://projecteuclid.org/euclid.afa/1466164865

Digital Object Identifier
doi:10.1215/20088752-3605321

Mathematical Reviews number (MathSciNet)
MR3513124

Zentralblatt MATH identifier
1367.46053

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

#### Citation

Yan, Cheng. The Hankel operators and noncommutative BMO spaces. Ann. Funct. Anal. 7 (2016), no. 3, 402--410. doi:10.1215/20088752-3605321. https://projecteuclid.org/euclid.afa/1466164865

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