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Another Weak Stone-Weierstrass Theorem for C*-Algebras

Published online by Cambridge University Press:  20 November 2018

George A. Elliott
George A. Elliott*
Affiliation:
Queen's University, Kingston, Ontario
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The purpose of this article is to present a new generalization of the classical Stone-Weierstrass theorem for commutative C*-algebras.

Under the assumption that B is a sub-C*-algebra of A separating the pure states of A and zero, Kaplansky has conjectured that B=A [4, p. 246]. He gave a proof for the case that A is postliminary ([4, Theorem 7.2]; see also [2, 11.1.8]). Glimm, Akemann, and Sakai have established the conjecture in the presence of various other additional hypotheses, most of which hold in the commutative case ([3], [1], [7]).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 3 , September 1972 , pp. 355 - 357
Copyright
Copyright © Canadian Mathematical Society 1972

References

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