Weak-closedness of subspaces of fourier-stieltjes algebras and weak-continuity of the restriction map

M. B. Bekka; E. Kaniuth; A. T. Lau; G. Schlichting

doi:10.1090/s0002-9947-98-01835-2

Weak-closedness of subspaces of fourier-stieltjes algebras and weak-continuity of the restriction map

M. B. Bekka, E. Kaniuth, A. T. Lau, G. Schlichting

Former organisations of the Department of Mathematics

Technical University of Munich

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15 Scopus citations

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.

Original language	English
Pages (from-to)	2277-2296
Number of pages	20
Journal	Transactions of the American Mathematical Society
Volume	350
Issue number	6
DOIs	https://doi.org/10.1090/s0002-9947-98-01835-2
State	Published - 1998

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AU - Lau, A. T.

AU - Schlichting, G.

PY - 1998

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N2 - 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.

AB - 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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ER -

Weak-closedness of subspaces of fourier-stieltjes algebras and weak-continuity of the restriction map

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