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- W2013044206 abstract "For a locally compact ${T_2}$ group $G$ which has an open subgroup of polynomial growth (e.g., $G$ a group that has a compact neighbourhood invariant under inner automorphisms or $G$ a compact extension of a locally compact nilpotent group) the intersection of the Pedersen ideal of the group ${C^ * }$-algebra with ${L^1}(G)$ is dense in ${L^1}(G)$ (Theorem 1). For groups with small invariant neighbourhoods this intersection is the smallest dense ideal of ${L^1}(G)$, and it consists exactly of those $f in {L^1}(G)$ whose Fourier transform vanishes outside some (closed) quasicompact subset of $hat G$ (Theorem 3); the Pedersen ideal of ${C^ * }(G)$ is described as the set of all $a in {C^ * }(G)$ for which $left { {pi in hat G:pi (a) ne 0} right }$ is contained in some (closed) quasicompact subset of $hat G$ (Theorem 2)." @default.
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- W2013044206 date "1981-01-01" @default.
- W2013044206 modified "2023-10-18" @default.
- W2013044206 title "Pedersen ideal and group algebras" @default.
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- W2013044206 doi "https://doi.org/10.1090/s0002-9939-1981-0620009-0" @default.
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