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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
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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}$.

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

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