# 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}
}
• Published 1 November 2016
• Mathematics
• arXiv: Functional Analysis
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
• 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 $\left( ## References SHOWING 1-10 OF 12 REFERENCES A general Beurling-Helson-Lowdenslager theorem on the disk A very general class of norms$\alpha$is defined and the Beurling-Helson-Lowdenslager invariant subspace theorem is extended, which describes the shift-invariant subspaces of the Hardy space and of the Lebesgue space. Lebesgue and Hardy spaces for symmetric norms I In this paper, we define and study a class$\mathcal{R}_{c}$of norms on$L^{\infty}\left( \mathbb{T}\right) $, called$continuous\ rotationally\ symmetric \ norms$, which properly contains the class Analytic functions and logmodular Banach algebras The first part of this paper presents a generalization of a portion of the theory of analytic functions in the unit disc. The theory to be extended consists of some basic theorems related to the Shifts on Hilbert spaces. Does every operator on an infinite-dimensional Hubert space have a non-trivial invariant subspace ? The question is still unanswered. A possible approach is to classify all invariant subspaces of all On two problems concerning linear transformations in hilbert space T n "0 We shall denote by Cf and C$ the closed linear manifolds spanned by { f}o and {T*'g}o, respectively; f , g being elements in H. This study is devoted to two general problems concerning the
Treatise on the shift operator
• Computer Science
• 1986
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