A Gromov-Hausdorff Distance between von Neumann Algebras and an Application to Free Quantum Fields
arXiv:1512.08709 · doi:10.1016/j.jfa.2016.12.029
Abstract
A distance between von Neumann algebras is introduced, depending on a further norm inducing the -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.
22 pages, no figures. To apper in the Journal of Functional Analysis
References in corpus (6)
- Metrics on State Spaces
- Metrics on states from actions of compact groups
- Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory
- On Gromov-Hausdorff convergence for operator metric spaces
- C*-algebraic quantum Gromov-Hausdorff distance
- The problem of completeness for Gromov-Hausdorff metrics on C*-algebras