On the Stone-Weierstrass theorem

Details On the Stone-Weierstrass theorem On the Stone-Weierstrass theorem

2011-11-13

arxiv.org/abs/1111.2980v1

Mathematics

Operator Algebras

This work dates from 2006, and some references may be out of date. Comments are welcome

Scientific paper

This paper extends a version of the Stone-Weierstrass theorem to more general C*-algebras. Namely, assume that A is a unital, not necessarily separable, C*-algebra, and B is a C*-subalgebra containing the unit element. Then, I prove that: If B separates the factorial states of A, then B=A. This generalizes a result of Popa and Longo for the case when A is separable. A true Stone-Weierstrass theorem would state that, if B separates the pure states of A, then B=A. This problem is open even in the separable case. The present paper relies on the more technical, foundational results in the companion article 'on Maximal Measures'

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