@article {37299,
	title = {Homomorphisms of L1 algebras and Fourier algebras},
	journal = {Journal of Mathematical Analysis and Applications },
	volume = {531},
	year = {2024},
	abstract = {We investigate conditions for the extendibility of continuous algebra homomorphisms ϕ from the Fourier algebra A(F ) of a locally compact group F to the Fourier-Stieltjes algebra B(G) of a locally compact group G to maps between the corresponding L<sup>$\infty$</sup> algebras which are weak* continuous. When ϕ is completely bounded and F is amenable, it is induced by a piecewise affine map α : Y {\textrightarrow} F where Y ⊆ G. We show that extendibility of ϕ is equivalent to α being an open map. <br>We also study the dual problem for contractive homomorphisms<br>ϕ : L<sup>1</sup> (F ) {\textrightarrow} M (G). We show that ϕ induces a w* continuous homomorphism between the von Neumann algebras of the groups if and only if the naturally associated map θ (Greenleaf [1965], Stokke [2011]) is a proper map.},
	url = {https://doi.org/10.1016/j.jmaa.2023.127824},
	author = {M. Anoussis, G. K. Eleftherakis, A. Katavolos}
}
