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Metric on the C*-algebras on a fixed Hilbert space
Let be a Hilbert space and denote the set of all bounded operators on . If and are linear subspaces of and denote their unit balls, respectively, the Kadison–Kastler distance between them is defined as,
The above notion of distance defines a metric on the space of C-algebras which is called the Kadison-Kastler metric.
References
Kadison, Richard V.; Kastler, Daniel (January 1972). "Perturbations of Von Neumann Algebras I Stability of Type". American Journal of Mathematics. 94 (1): 38. doi:10.2307/2373592. ISSN0002-9327. JSTOR2373592.