Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-28T00:50:42.175Z Has data issue: false hasContentIssue false
  • English
  • Français

Mackey Borel Structure for the Quasi-Dual of a Separable C*-Algebra

Published online by Cambridge University Press:  20 November 2018

Herbert Halpern
Herbert Halpern*
Affiliation:
University of Cincinnati, Cincinnati, Ohio
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let A be a separable C*-algebra. Two representations π and π1 of A on the Hilbert spaces H and H1, respectively are said to be quasi-equivalent (denoted by π ~ π1) if projections of H ⊕ H1 on the invariant subspaces H and H1 of (π ⊕ π1)(A) have the same central support in the commutant (π ⊕ π1) (A)′ of (π ⊕ π1) (A), or equivalently, if there is an isomorphism ϕ of π(A)″ onto π1(A)″ such that ϕ(π(x)) = π(x) for all x ∊ A (cf. [5, § 5]). A representation π of A is said to be a factor representation if the center of π(A)″ consists of scalar multiples of the identity.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 3 , June 1974 , pp. 621 - 628
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Auslander, L. and Moore, C. C., Unitary representation of solvable Lie groups, Memoirs Amer. Math. Soc. 62 (1966).Google Scholar
2. Bourbaki, N., Topologie générale Ch. 9., Actualités Scientifiques et industrielles No. 1045 (Hermann, Paris, 1958).Google Scholar
3. Combes, F., Représentations d'une C*-algèbres et formes linéaires positives, C. R. Acad. Sci. Paris Ser. A-B 260 (1965), 5993–5996.Google Scholar
4. Dixmier, J., Quasi-dual d'une ideal dans une C*-algèbre, Bull. Sci. Math. 87 (1963), 7–11.Google Scholar
5. Dixmier, J., Les C*-algèbres et leurs représentations (Gauthier-Villars, Paris, 1964).Google Scholar
6. Efïros, E., Transformation groups and C*-algebras, Ann. of Math. 81 (1965), 38–55.Google Scholar
7. Efïros, E., The canonical measures for a separable C*-algebra, Amer. J. Math. 92 (1970), 56–60.Google Scholar
8. Gardner, L. T., On the Mackey Borel structure, Can. J. Math. 23 (1971), 674–678.Google Scholar
9. Halpern, H., Open projections and Borel structures for C*-algebras (to appear in Pacific J. Math.).Google Scholar
10. Sakai, S., C*-algebras and W*-algebras (Springer-Verlag, New York, 1971).Google Scholar