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arXiv · 1104.2953

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

Yemon Choi·Ebrahim Samei
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Abstract

We observe that for a large class of non-amenable groups $G$, one can find bounded representations of $A(G)$ on 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 Helson set which takes account of operator space structure. In particular, we show that if $G$ is virtually abelian, then the restriction algebra $A_G(E)$ is completely isomorphic to an operator algebra if and only if $E$ is finite.

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Yemon Choi, Ebrahim Samei. 2011-04-15. Quotients of Fourier algebras, and representations which are not completely bounded. https://doi.org/10.1090/s0002-9939-2013-11974-x

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