Abstract
LetG be a locally compact group with polynomial growth and symmetricL 1-algebra andN a closed normal subgroup ofG. LetF be a closedG-invariant subset of Prim* L 1(N) andE={kerπ;π∈Ĝ with π|N(k(F))=0}. We prove thatE is a spectral subset of Prim* L 1(G) ifF is spectral. Moreover we give the following application to the ideal theory ofL 1(G). Suppose that, in addition,N is CCR andG/N is compact. Then all primary ideals inL 1(G) are maximal, provided allG-orbits in Prim* L 1(N) are spectral.
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Dedicated to Professor Elmar Thoma on the occasion of his 60th birthday
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Bekka, M.E.B. The projection theorem for spectral sets. Monatshefte für Mathematik 101, 1–10 (1986). https://doi.org/10.1007/BF01326842
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DOI: https://doi.org/10.1007/BF01326842