Abstract
We show that the crossed product between a C ∗-algebra A and a locally compact abelian group G with a representation α as automorphisms of A is a prime C ∗-algebra (any two nonzero ideals have a nonzero intersection) if and only if two conditions are satisfied: (a) A is G-prime (any two nonzero G-invariant ideals of A have a nonzero intersection); and (b) the Connes spectrum Γ(α) of α equals the whole dual group of G.
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