2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70672The 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.Operator AlgebrasCategory TheoryRings and AlgebrasPrimary 46L05; Secondary 06F07, 46L85, 46M15, 54A05text