An Extension of the ChenBeurlingHelsonLowdenslager Theorem
Abstract
Yanni Chen extended the classical BeurlingHelsonLowdenslager 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 measure on $\mathbb{T}$, such that $\alpha\geq c\Vert\cdot\Vert_{1,\lambda}$ for some $0<c\leq1.$
 Publication:

arXiv eprints
 Pub Date:
 October 2016
 arXiv:
 arXiv:1611.00357
 Bibcode:
 2016arXiv161100357F
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Operator Algebras