Quotients of the Fourier algebra, and representations that are not completely bounded

Details Quotients of the Fourier algebra, and representations that are not completely bounded Quotients of the Fourier algebra, and representations that are not completely bounded

2011-04-15

arxiv.org/abs/1104.2953v2

Mathematics

Functional Analysis

9 pages, submitted. Uses Paul Taylor's diagrams.sty macros. v2: 11 pages, resubmitted. Appendix added, giving an alternative p

Scientific paper

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 $A(E)$ is completely isomorphic to an operator algebra if and only if $E$ is finite.

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