Abstract
Let G be a locally compact group, A (G) its Fourier algebra and Acb (G) the closure of A (G) in the space of completely bounded multipliers of A (G). We show that the Fourier algebras of weakly amenable, non-amenable groups are not approximately amenable. We also prove that A (G) is operator approximately biprojective if and only if G is discrete. Finally, we study various (operator) cohomological properties and its related (operator) homological properties of the algebra Acb (G).
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