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Groups of automorphisms with spectrum condition and the lifting problem

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Abstract

We show that a continuous one-parameter group {α t } of automorphisms of a separableC*-algebraA satisfies a spectrum condition if and only if it is the limit, pointwise onA, uniformly on compact subsets of IR of a sequence of inner automorphism groups whose positive generators do not increase too fast. Moreover we prove in this case that if π is a surjective morphism of a separableC*-algebraB onA then there is a similar group\(\{ \bar \alpha _t \} \) of automorphisms ofB such that\(\pi \circ \bar \alpha _t = \alpha _t \circ \pi \) for allt.

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Communicated by H. Araki

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Olesen, D., Pedersen, G.K. Groups of automorphisms with spectrum condition and the lifting problem. Commun.Math. Phys. 51, 85–95 (1976). https://doi.org/10.1007/BF01609053

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  • DOI: https://doi.org/10.1007/BF01609053

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