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Operator Amenability of the Fourier Algebra in the cb-Multiplier Norm

  • Brian E. Forrest (a1), Volker Runde (a1) and Nico Spronk (a2)
Abstract

Let G be a locally compact group, and let A cb(G) denote the closure of A(G), the Fourier algebra of G, in the space of completely boundedmultipliers of A(G). If G is a weakly amenable, discrete group such that C*(G) is residually finite-dimensional, we show that A cb(G) is operator amenable. In particular, A cb() is operator amenable even though , the free group in two generators, is not an amenable group. Moreover, we show that if G is a discrete group such that A cb(G) is operator amenable, a closed ideal of A(G) is weakly completely complemented in A(G) if and only if it has an approximate identity bounded in the cb-multiplier norm.

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References
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