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–Maréchal 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.
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