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Quotients of Fourier algebras, and representations which are not completely bounded

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>20/03/2013
<mark>Journal</mark>Proceedings of the American Mathematical Society
Issue number7
Volume141
Number of pages10
Pages (from-to)2379-2388
Publication StatusPublished
<mark>Original language</mark>English

Abstract

We observe that for a large class of non-amenable groups G, one can find bounded representations of A(G) on a Hilbert space which are not completely bounded. We also consider restriction algebras obtained from A(G), equipped with the natural operator space structure, and ask whether such algebras can be completely isomorphic to operator algebras. Partial results are obtained using a modified notion of the Helson set which takes into account operator space structure. In particular, we show that when G is virtually abelian and E is a closed subset, the restriction algebra AG(E) is completely isomorphic to an operator algebra if and only if E is finite.