Locally convex algebras which determine a locally compact group
Studia Mathematica, Tome 233 (2016) no. 3, p. 197.

Voir la notice de l'article dans European Digital Mathematics Library

There are several algebras associated with a locally compact group 𝓖 which determine 𝓖 in the category of topological groups, such as L¹(𝓖), M(𝓖), and their second duals. In this article we add a fairly large family of locally convex algebras to this list. More precisely, we show that for two infinite locally compact groups 𝓖₁ and 𝓖₂, there are infinitely many locally convex topologies τ₁ and τ₂ on the measure algebras M(𝓖₁) and M(𝓖₂), respectively, such that (M(𝓖₁),τ₁)** is isometrically isomorphic to (M(𝓖₂),τ₂)** if and only if 𝓖₁ and 𝓖₂ are topologically isomorphic. In particular, this leads to a new proof of Ghahramani-Lau's isometrical isomorphism theorem for compact groups, different from those of Ghahramani and J. P. McClure (2006) and Dales et al. (2012).
Classification : 43A10, 43A20, 43A22
Mots-clés : locally compact groups, measure algebra, generalized functions vanishing at infinity, second dual 
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Gholam Hossein Esslamzadeh; Hossein Javanshiri; Rasoul Nasr-Isfahani. Locally convex algebras which determine a locally compact group. Studia Mathematica, Tome 233 (2016) no. 3, p. 197. https://geodesic-test.mathdoc.fr/item/STUMA_2016__233_3_286150/