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Locally convex algebras which determine a locally compact group

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Esslamzadeh G., Javanshiri H., Nasr-Isfahani R.

Studia Mathematica

2016

tom 233

nr 3

197-207

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).

Ograniczanie wyników

1 Studia Mathematica

1 Esslamzadeh G.

1 Javanshiri H.

1 Nasr-Isfahani R.

1 2016

Wyniki wyszukiwania

Locally convex algebras which determine a locally compact group