LAUSR

Abstract A distance between von Neumann algebras is introduced, depending on a further norm inducing the w ⁎ -topology on bounded sets. Such notion is related both with the Gromov–Hausdorff distance for quantum metric spaces of Rieffel [24] and with the Effros–Marechal topology [10] , [19] on the von Neumann algebras acting on a Hilbert space. This construction is tested on the local algebras of free quantum fields endowed with norms related with the Buchholz–Wichmann nuclearity condition [3] , showing the continuity of such algebras w.r.t. the mass parameter.