Abstract

For A C^*-algebra and M(A) its multiplier algebra, the weak topologies σ(M(A),A^*) and σ(A^*,M(A)) are shown to have the Krein property, claiming the compactness of the closed convex hull of every compact set. This has relevant consequences concerning the analytic generator of strictly continuous one-parameter groups of strictly continuous linear operators on M(A).

Furthermore, it is proved that there exists an one-to-one correspondence between surjective linear isometries on A and strictly bicontinuous, surjective linear isometries on M(A), as well as between strongly continuous respectively strictly continuous locally compact groups of them. In the case of connected groups, they all arise from *-automorphism groups by perturbation with a cocycle.

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