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  • 1504.03597v2

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Realization of compact spaces as cb-Helson sets

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>02/2016
<mark>Journal</mark>Annals of Functional Analysis
Issue number1
Volume7
Number of pages12
Pages (from-to)158-169
Publication StatusPublished
Early online date22/12/15
<mark>Original language</mark>English

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.