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## Studia Mathematica

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## Locally convex algebras which determine a locally compact group

### Tom 233 / 2016

Studia Mathematica 233 (2016), 197-207 MSC: Primary 43A10, 43A20; Secondary 43A22. DOI: 10.4064/sm7879-4-2016 Opublikowany online: 21 June 2016

#### Streszczenie

There are several algebras associated with a locally compact group $\mathcal G$ which determine ${\mathcal G}$ in the category of topological groups, such as $L^1({\mathcal G})$, $M({\mathcal G})$, 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 ${\mathcal G}_1$ and ${\mathcal G}_2$, there are infinitely many locally convex topologies $\tau _1$ and $\tau _2$ on the measure algebras $M({\mathcal G}_1)$ and $M({\mathcal G}_2)$, respectively, such that $(M({\mathcal G}_1),\tau _1)^{**}$ is isometrically isomorphic to $(M({\mathcal G}_2),\tau _2)^{**}$ if and only if ${\mathcal G}_1$ and ${\mathcal G}_2$ 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).

#### Autorzy

• Gholam Hossein EsslamzadehDepartment of Mathematics
Faculty of Sciences
Shiraz University
Shiraz 71454, Iran
e-mail
• Hossein JavanshiriDepartment of Mathematics
Yazd University
P.O. Box 89195-741
Yazd, Iran
e-mail
• Rasoul Nasr-IsfahaniDepartment of Mathematical Sciences
Isfahan University of Technology
Isfahan 84156-83111, Iran
and
School of Mathematics
Institute for Research in Fundamental Sciences (IPM)
P.O. Box 19395-5746
Tehran, Iran
e-mail

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