Geodesic
On Open Projections of GCR Algebras
Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 978-982

Voir la notice de l'article provenant de la source Cambridge University Press

Throughout this paper will denote a C*-algebra and will denote its second dual, which is identified with the enveloping von Neumann algebra of . A projection E in is said to be open if it supports a left ideal in , that is, if E = - for some left ideal in . Here the bar - means the stong closure. When has a unit, this definition coincides with the definition of Akemann [1, Definition II. 1]. In the sequel, we shall solely be concerned with two-sided ideals, and consequently central projections [4, I, § 3, Corollary 3 of Theorem 2]. Our aim is to show that is CCR if and only if the open central projections are strongly dense in the set of central projections on . 
Digernes, Trond; Halpern, Herbert. On Open Projections of GCR Algebras. Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 978-982. doi: 10.4153/CJM-1972-098-6
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[1] 1. Akemann, C., The general Stone-Weierestrass problem, J. Functional Analysis 4 (1969), 277–294. Google Scholar

[2] 2. Bade, W. G., On Boolean algebras of projections and algebras of operators, Trans. Amer. Math. Soc. 80 (1955), 345–360. Google Scholar

[3] 3. Dixmier, J., Les C*-algebres et leurs representations (Gauthier-Villars, Paris, 1964). Google Scholar

[4] 4. Dixmier, J., Les algebres d'operateurs dans l’espace Hilbertien (Gauthier-Villars, Paris, 2e édition, 1969). Google Scholar

[5] 5. Elliott, G., Ideal preserving automorphisms of postliminary C*-algebras, Proc. Amer. Math. Soc. 27 (1971), 107–109. Google Scholar

[6] 6. Halpern, H., A generalized dual for a C*-algebra, Trans. Amer. Math. Soc. 153 (1971), 139–156. Google Scholar

[7] 7. Lance, E., Automorphisms of postliminary C*-algebras, Pacific J. Math. 23 (1967), 547–555. Google Scholar

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