We prove that if open subgroups of the groups of invertible elements in two Fourier-Stieltjes algebras are isometric as metric spaces, then the underlying locally compact groups are topologically isomorphic. We describe the structure of isometric real algebra isomorphisms between Fourier-Stieltjes algebras and apply it to prove the above result.
On 2-local *-automorphisms and 2-local isometries of B(H)
A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa
Inversion problem in measure and Fourier-Stieltjes algebras
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