A new characterization of separable GCR-algebras
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Abstract:
It is shown that a separable ${C^ \ast }$-algebra $\mathfrak {A}$ is GCR if and only if the set of central projections in its enveloping von Neumann algebra $\mathfrak {B}$ is generated, as a complete Boolean algebra, by the set of open, central projections in $\mathfrak {B}$.References
- Charles A. Akemann, The general Stone-Weierstrass problem, J. Functional Analysis 4 (1969), 277–294. MR 0251545, DOI 10.1016/0022-1236(69)90015-9
- Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173 —, Les algebres d’opérateurs dans l’espace Hilbertien, 2ième éd., Gauthier-Villars, Paris, 1969.
- James Glimm, Type I $C^{\ast }$-algebras, Ann. of Math. (2) 73 (1961), 572–612. MR 124756, DOI 10.2307/1970319 H. Halpern and T. Digernes, On open projections for ${C^\ast }$-algebras (to appear).
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 448-450
- MSC: Primary 46L05
- DOI: https://doi.org/10.1090/S0002-9939-1972-0310656-2
- MathSciNet review: 0310656