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arXiv · 1512.08709

A Gromov-Hausdorff Distance between von Neumann Algebras and an Application to Free Quantum Fields

D. Guido·N. Marotta·G. Morsella·L. Suriano
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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 and with the Effros-Marechal topology 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, showing the continuity of such algebras w.r.t. the mass parameter.

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D. Guido, N. Marotta, G. Morsella, L. Suriano. 2015-12-29. A Gromov-Hausdorff Distance between von Neumann Algebras and an Application to Free Quantum Fields. https://doi.org/10.1016/j.jfa.2016.12.029

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