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).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm7879-4-2016,
author = {Gholam Hossein Esslamzadeh and Hossein Javanshiri and Rasoul Nasr-Isfahani},
title = {Locally convex algebras which determine a locally compact group},
journal = {Studia Mathematica},
volume = {233},
year = {2016},
pages = {197-207},
zbl = {06602796},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm7879-4-2016}
}
Gholam Hossein Esslamzadeh; Hossein Javanshiri; Rasoul Nasr-Isfahani. Locally convex algebras which determine a locally compact group. Studia Mathematica, Tome 233 (2016) pp. 197-207. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm7879-4-2016/