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