Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A new characterization of separable GCR-algebras

Author: Trond Digernes
Journal: Proc. Amer. Math. Soc. 36 (1972), 448-450
MSC: Primary 46L05
MathSciNet review: 0310656
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] C. A. Akemann, The general Stone-Weierstrass problem, J. Functional Analysis 4 (1969), 277-294. MR 40 #4772. MR 0251545 (40:4772)
  • [2] J. Dixmier, Les $ {C^\ast}$-algèbres et leurs représentations, Cahiers Scientifiques, fasc. 29, Gauthier-Villars, Paris, 1964. MR 30 #1404. MR 0171173 (30:1404)
  • [3] -, Les algebres d'opérateurs dans l'espace Hilbertien, 2ième éd., Gauthier-Villars, Paris, 1969.
  • [4] J. Glimm, Type I $ {C^\ast}$-algebras, Ann. of Math. (2) 73 (1961), 572-612. MR 23 #A2066. MR 0124756 (23:A2066)
  • [5] H. Halpern and T. Digernes, On open projections for $ {C^\ast}$-algebras (to appear).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L05

Retrieve articles in all journals with MSC: 46L05

Additional Information

Keywords: $ {C^ \ast }$-algebra, enveloping von Neumann algebra, open projections, GCR-algebra
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society