Accepted author manuscript, 168 KB, PDF document
Available under license: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
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 -