Abstract
As shown by Cohen (1960) and Ilie and Spronk (2005), for locally compact groups G and H, there is a one-to-one correspondence between the completely bounded homomorphisms of their respective Fourier and Fourier–Stieltjes algebras φ:A(G)→B(H) and piecewise affine continuous maps α:Y⊆H→G. Using elementary arguments, we show that several (locally compact) group-theoretic properties, including amenability, are preserved by certain continuous piecewise affine maps. We discuss these results in relation to Fourier algebra homomorphisms.
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