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DERIVATIONS, DYNAMICAL SYSTEMS, AND SPECTRAL RESTRICTIONS
AKITAKA KISHIMOTO and DEREK W. ROBINSON
Vol. 56, No. 1 (October 21, 1985), pp. 83-95
Published by: Mathematica Scandinavica
Stable URL: http://www.jstor.org/stable/24491545
Page Count: 13
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Let (𝔄, G, α) be a C*-dynamical system with G locally compact abelian and consider a closed *-derivation δ commuting with α. If 𝔄 is α-prime and Ĝ/Γ(α) compact, then D(δ) contains the spectral subspaces 𝔄α(K) of α corresponding to compacts K ⊂ Ĝ if, and only if, δ generates a bounded perturbation of a one-parameter subgroup ϱ of αG. Alternatively if 𝔄 is abelian and G = R the spectral condition D(δ)⫆𝔄α(K) implies that δ generates a group β obtained from α by a rescaling of the corresponding flow.
Mathematica Scandinavica © 1985 Mathematica Scandinavica