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Realization of compact spaces as cb-Helson sets

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Realization of compact spaces as cb-Helson sets. / Choi, Yemon.
In: Annals of Functional Analysis, Vol. 7, No. 1, 02.2016, p. 158-169.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

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Choi, Y 2016, 'Realization of compact spaces as cb-Helson sets', Annals of Functional Analysis, vol. 7, no. 1, pp. 158-169. https://doi.org/10.1215/20088752-3429526

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Vancouver

Choi Y. Realization of compact spaces as cb-Helson sets. Annals of Functional Analysis. 2016 Feb;7(1):158-169. Epub 2015 Dec 22. doi: 10.1215/20088752-3429526

Author

Choi, Yemon. / Realization of compact spaces as cb-Helson sets. In: Annals of Functional Analysis. 2016 ; Vol. 7, No. 1. pp. 158-169.

Bibtex

@article{525a6807fc784e1aa8ba72694979b2fe,
title = "Realization of compact spaces as cb-Helson sets",
abstract = "We show that, given a compact Hausdorff space $\Omega$, there is a compact group ${\mathbb G}$ and a homeomorphic embedding of $\Omega$ into ${\mathbb G}$, such that the restriction map ${\rm A}({\mathbb G})\to C(\Omega)$ is a complete quotient map of operator spaces. In particular, this shows that there exist compact groups which contain infinite cb-Helson subsets, answering a question raised in [Choi--Samei, Proc. AMS 2013; cf. http://arxiv.org/abs/1104.2953]. A negative result from the same paper is also improved.",
keywords = "Fourier algebra, Helson set, Operator space",
author = "Yemon Choi",
year = "2016",
month = feb,
doi = "10.1215/20088752-3429526",
language = "English",
volume = "7",
pages = "158--169",
journal = "Annals of Functional Analysis",
issn = "2008-8752",
publisher = "Tusi Mathematical Research Group",
number = "1",

}

RIS

TY - JOUR

T1 - Realization of compact spaces as cb-Helson sets

AU - Choi, Yemon

PY - 2016/2

Y1 - 2016/2

N2 - We show that, given a compact Hausdorff space $\Omega$, there is a compact group ${\mathbb G}$ and a homeomorphic embedding of $\Omega$ into ${\mathbb G}$, such that the restriction map ${\rm A}({\mathbb G})\to C(\Omega)$ is a complete quotient map of operator spaces. In particular, this shows that there exist compact groups which contain infinite cb-Helson subsets, answering a question raised in [Choi--Samei, Proc. AMS 2013; cf. http://arxiv.org/abs/1104.2953]. A negative result from the same paper is also improved.

AB - We show that, given a compact Hausdorff space $\Omega$, there is a compact group ${\mathbb G}$ and a homeomorphic embedding of $\Omega$ into ${\mathbb G}$, such that the restriction map ${\rm A}({\mathbb G})\to C(\Omega)$ is a complete quotient map of operator spaces. In particular, this shows that there exist compact groups which contain infinite cb-Helson subsets, answering a question raised in [Choi--Samei, Proc. AMS 2013; cf. http://arxiv.org/abs/1104.2953]. A negative result from the same paper is also improved.

KW - Fourier algebra

KW - Helson set

KW - Operator space

U2 - 10.1215/20088752-3429526

DO - 10.1215/20088752-3429526

M3 - Journal article

VL - 7

SP - 158

EP - 169

JO - Annals of Functional Analysis

JF - Annals of Functional Analysis

SN - 2008-8752

IS - 1

ER -