Journal article
Extensions of unbounded -derivations in UHF C-algebras
Journal of functional analysis, Vol.45(3), pp.341-356
1982
DOI: 10.1016/0022-1236(82)90010-6
Abstract
We consider unbounded ∗ -derivations δ in UHF- C ∗ -algebras A =(∪ ∞ n =1 A n ) − ) with dense domain. If ϕ n : A → A n denotes the conditional expectations onto the finite type I factors A n , then we introduce a weak-commutativity condition for δ and the sequence ( ϑ n ). As a consequence of this condition on δ we establish the existence of an extension derivation δ′ which is the infinitesimal generator of a strongly continuous one-parameter group, α: R → Aut( A ), of ∗ -automorphisms, i.e., δ′(x) = (d dt) α t (x)¦ t = 0 for x ϵ D ( δ ′). Special properties of α (alias δ′) are considered. We show that AF-algebras are associated to proper restrictions δ of derivations δ′ of product type. We then turn to the extendability problem for quasifree derivations in the CAR-algebra. There, extensions δ′ are calculated which generate strongly continuous semigroups of ∗ -homomorphisms. These semigroups do not extend to one-parameter groups unless the implementing symmetric operator in one-particle space is already self-adjoint.
Details
- Title: Subtitle
- Extensions of unbounded -derivations in UHF C-algebras
- Creators
- Palle E.T Jørgensen
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.45(3), pp.341-356
- DOI
- 10.1016/0022-1236(82)90010-6
- ISSN
- 1096-0783
- eISSN
- 1096-0783
- Language
- English
- Date published
- 1982
- Academic Unit
- Mathematics
- Record Identifier
- 9983986087602771
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