Journal article
A C*-algebraic Schoenberg theorem
Annales de l'Institut Fourier, Vol.34(3), pp.155-187
1984
DOI: 10.5802/aif.981
Abstract
Let 𝔄 be a �*-algebra, � a compact abelian group, � an action of � by *-automorphisms of 𝔄,𝔄� the fixed point algebra of � and 𝔄� the dense sub-algebra of �-finite elements in 𝔄. Further let � be a linear operator from 𝔄� into 𝔄 which commutes with � and vanishes on 𝔄�. We prove that � is a complete dissipation if and only if � is closable and its closure generates a �0-semigroup of completely positive contractions. These complete dissipations are classified in terms of certain twisted negative definite maps from the dual group �^ into dissipative operators affiliated with the center of the multiplier algebra of 𝔄�. We also argue that the complete dissipation property is strictly stronger than the usual dissipation property, except in special circumstances such as when 𝔄 is abelian.
Details
- Title: Subtitle
- A C*-algebraic Schoenberg theorem
- Creators
- Ola BratteliPalle E. T. JorgensenAkitaka KishimotoDonald W. Robinson
- Resource Type
- Journal article
- Publication Details
- Annales de l'Institut Fourier, Vol.34(3), pp.155-187
- DOI
- 10.5802/aif.981
- ISSN
- 0373-0956
- Language
- English
- Date published
- 1984
- Academic Unit
- Mathematics
- Record Identifier
- 9984242339202771
Metrics
19 Record Views