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- W2092438173 abstract "If G is a locally compact group, denote its Fourier-Stieltjes algebra by B(G) and its Fourier algebra by Λ(G). If G is compact, then B(G) = Λ(G) and σ(B(G)), the spectrum o! B(G), is G. If G is not compact then σ(B(G)) contains partial isometries and projections different from e, the identity of G. More generally, σ(B(G)) is closed under operations that commute with representing and the taking of tensor products. It is shown that σ(B(G)) contains a smallest positive element, zF; and that g G G Cσ(B(G))h+z Fg G σ(B(G))zF is an epimorphism of G into G, the almost periodic compactification of G. A structure theorem is given for the closed, bi-translation, invariant subspaces of B(G). In so doing we introduce the concepts of inverse Fourier transform localized at TΓ, and the standardization of TΓ, where TΓ is a continuous, unitary representation of G." @default.
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- W2092438173 date "1975-05-01" @default.
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- W2092438173 title "On the structure of the Fourier-Stieltjes algebra" @default.
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- W2092438173 doi "https://doi.org/10.2140/pjm.1975.58.267" @default.
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