# An Extension of the Chen-Beurling-Helson-Lowdenslager Theorem

@article{Fan2016AnEO, title={An Extension of the Chen-Beurling-Helson-Lowdenslager Theorem}, author={Haihui Fan and Donald W. Hadwin and Wenjing Liu}, journal={arXiv: Functional Analysis}, year={2016} }

Yanni Chen extended the classical Beurling-Helson-Lowdenslager Theorem for Hardy spaces on the unit circle $\mathbb{T}$ defined in terms of continuous gauge norms on $L^{\infty}$ that dominate $\Vert\cdot\Vert_{1}$. We extend Chen's result to a much larger class of continuous gauge norms. A key ingredient is our result that if $\alpha$ is a continuous normalized gauge norm on $L^{\infty}$, then there is a probability measure $\lambda$, mutually absolutely continuous with respect to Lebesgue…

## One Citation

An extension of the Beurling-Chen-Hadwin-Shen theorem for noncommutative Hardy spaces associated with finite von Neumann algebras

- Mathematics
- 2016

In 2015, Yanni Chen, Don Hadwin and Junhao Shen proved a noncommutative version of Beurling's theorems for a continuous unitarily invariant norm $% \alpha $ on a tracial von Neumann algebra $\left(…

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