Abstract
We show that a full Hilbert C∗-module X can be embedded in the multiplier module of the crossed product of X by a continuous action η of a locally compact group G on X. Also, we show that there is a bijective correspondence between nondegenerate covariant representations of X and nondegenerate representations of the crossed product of X by η, and moreover, this correspondence preserves the irreducibility and unitary equivalence.
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