2004/03/31 by David Kruml, Pedro Resende
Mathematics · #math.OA #math.CT #math.RA #msc:46L05 #msc:06F07 #msc:46L85 #msc:46M15 #msc:54A05
published as Cah. Topol. Géom. Différ. Catég. 45 (2004) 287-296.
arxiv created 2004/03/31 · arxiv updated 2009/12/01
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.