Journal article
Unbounded derivations tangential to compact groups of automorphisms, II
Journal of functional analysis, Vol.61(3), pp.247-289
1985
DOI: 10.1016/0022-1236(85)90022-9
Abstract
Let G be a compact abelian group, and τ an action of G on a C ∗ -algebra U , such that U τ (γ) U τ (γ) ∗ = U τ (0) U τ for all γ ϵ G ̂ , where U τ (γ) is the spectral subspace of U corresponding to the character γ on G . Derivations δ which are defined on the algebra U F of G -finite elements are considered. In the special case δ¦ U τ = 0 these derivations are characterized by a cocycle on G ̂ with values in the relative commutant of U τ in the multiplier algebra of U , and these derivations are inner if and only if the cocycles are coboundaries and bounded if and only if the cocycles are bounded. Under various restrictions on G and τ properties of the cocycle are deduced which again give characterizations of δ in terms of decompositions into generators of one-parameter subgroups of τ ( G ) and approximately inner derivations. Finally, a perturbation technique is devised to reduce the case δ( U F ) ⊆ U F to the case δ( U F ) ⊆ U F and δ¦ U τ = 0. This is used to show that any derivation δ with D(δ) = U F is wellbehaved and, if furthermore G = T 1 and δ( U F ) ⊆ U F the closure of δ generates a one-parameter group of ∗ -automorphisms of U . In the case G = T d , d = 2, 3,… (finite), and δ( U F ) ⊆ U F it is shown that δ extends to a generator of a group of ∗ -automorphisms of the σ-weak closure of U in any G -covariant representation.
Details
- Title: Subtitle
- Unbounded derivations tangential to compact groups of automorphisms, II
- Creators
- Ola BratteliFrederick M GoodmanPalle E.T Jørgensen
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.61(3), pp.247-289
- DOI
- 10.1016/0022-1236(85)90022-9
- ISSN
- 1096-0783
- eISSN
- 1096-0783
- Language
- English
- Date published
- 1985
- Academic Unit
- Mathematics
- Record Identifier
- 9983985827702771
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