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Locally convex algebras which determine a locally compact group

Tom 233 / 2016

Gholam Hossein Esslamzadeh, Hossein Javanshiri, Rasoul Nasr-Isfahani 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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