Weak*-closedness of subspaces of Fourier-Stieltjes algebras and weak*-continuity of the restriction map

Bekka, M.; Kaniuth, E.; Lau, A.; Schlichting, G.

doi:10.1090/S0002-9947-98-01835-2

Weak-closedness of subspaces of Fourier-Stieltjes algebras and weak-continuity of the restriction map
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by M. B. Bekka, E. Kaniuth, A. T. Lau and G. Schlichting

Trans. Amer. Math. Soc. 350 (1998), 2277-2296

DOI: https://doi.org/10.1090/S0002-9947-98-01835-2

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Abstract:

Let $G$ be a locally compact group and $B(G)$ the Fourier-Stieltjes algebra of $G$. We study the problem of how weak*-closedness of some translation invariant subspaces of $B(G)$ is related to the structure of $G$. Moreover, we prove that for a closed subgroup $H$ of $G$, the restriction map from $B(G)$ to $B(H)$ is weak*-continuous only when $H$ is open in $G$.

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