On quantales that classify C*-algebras

Details On quantales that classify C*-algebras On quantales that classify C*-algebras

2004-03-31

arxiv.org/abs/math/0404001v1

Cah. Topol. G\'eom. Diff\'er. Cat\'eg. 45 (2004) 287-296.

Mathematics

Operator Algebras

Scientific paper

The functor Max of Mulvey assigns to each unital C*-algebra A the unital involutive quantale Max A of closed linear subspaces of A, and it has been remarked that it classifies unital C*-algebras up to *-isomorphism. In this paper we provide a proof of this and of the stronger fact that for every isomorphism u : Max A -> Max B of unital involutive quantales there is a *-isomorphism u' : A -> B such that Max u' coincides with u when restricted to the left-sided elements of Max A. But we also show that isomorphisms u : Max A -> Max B may exist for which no isomorphism v : A -> B is such that Max v = u.

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