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

Herbert Halpern

doi:10.4153/cjm-1974-059-9

journal article Jun 01, 1974

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

Herbert Halpern

Canadian Journal of Mathematics Vol. 26 No. 3 pp. 621-628 · Canadian Mathematical Society

View at Publisher Save 10.4153/cjm-1974-059-9

Abstract

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.

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References

10

[1]

Bourbaki (1958)

[2]

Combes "Représentations d'une C*-algèbres et formes linéaires positives" C. R. Acad. Sci. Paris Ser. A-B (1965)

[3]

10.2307/1970381

[4]

Auslander "Unitary representation of solvable Lie groups" Memoirs Amer. Math. Soc. (1966)

[5]

10.2307/2373497

[6]

Sakai (1971)

[7]

Dixmier "Quasi-dual d'une ideal dans une C*-algèbre" Bull. Sci. Math. (1963)

[8]

Halpern H. , Open projections and Borel structures for C*-algebras (to appear in Pacific J. Math.).

[9]

10.4153/cjm-1971-074-9

[10]

Dixmier (1964)

Metrics

6

Citations

10

References

Details

Published: Jun 01, 1974
Vol/Issue: 26(3)
Pages: 621-628
License: View

Authors

H

Herbert Halpern

Cite This Article

Herbert Halpern (1974). Mackey Borel Structure for the Quasi-Dual of a Separable C*-Algebra. Canadian Journal of Mathematics, 26(3), 621-628. https://doi.org/10.4153/cjm-1974-059-9

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

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