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<p>In the paper, we describe the structure of isometric real algebra isomorphisms between Fourier–Stieltjes algebras. By applying it, we see that if open subgroups of the groups of invertible elements in two Fourier–Stieltjes algebras are isometric as metric spaces, the underlying locally compact groups are topologically isomorphic.</p>

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Identification of Locally Compact Groups via the Metric Structure of the Groups of Invertible Elements in Fourier–Stieltjes Algebras

  • 期刊论文

  • 发表日期：

    2025年5月13日

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  • Osamu Hatori,
  • Shiho Oi

摘要

In the paper, we describe the structure of isometric real algebra isomorphisms between Fourier–Stieltjes algebras. By applying it, we see that if open subgroups of the groups of invertible elements in two Fourier–Stieltjes algebras are isometric as metric spaces, the underlying locally compact groups are topologically isomorphic.