Abstract
We define a sequence of functions, namely, tame cuts, in the Fourier algebra A(G) of a locally compact group G , which satisfies certain convergence and growth conditions. This new consideration allows us to give a group admitting a Fourier multiplier that is not completely bounded. Furthermore, we show that the induction map MA(\Gamma)\rightarrow MA(G) is not always continuous. We also show how Liao’s property (T_{\mathrm{Schur}},G,K) opposes tame cuts. Some examples are provided.
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