We show that, given a compact Hausdorff space , there is a compact group and a homeomorphic embedding of into , such that the restriction map 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 by Choi and Samei. A negative result from that paper is also improved.
"Realization of compact spaces as cb-Helson sets." Ann. Funct. Anal. 7 (1) 158 - 169, February 2016. https://doi.org/10.1215/20088752-3429526