Kadison and Kastler introduced a natural metric on the collection of all C*-subalgebras of the bounded operators on a separable Hilbert space. They conjectured that sufficiently close algebras are unitarily conjugate. We establish this conjecture when one algebra is separable and nuclear. We also consider one-sided versions of these notions, and we obtain embeddings from certain near inclusions involving separable nuclear C*-algebras. At the end of the paper we demonstrate how our methods lead to improved characterisations of some of the types of algebras that are of current interest in the classification programme.
This paper provides the details of the results announced in Christensen et al. Proc. Natl. Acad. Sci. USA 107 (2010), 587–591.
"Perturbations of nuclear C*-algebras." Acta Math. 208 (1) 93 - 150, 2012. https://doi.org/10.1007/s11511-012-0075-5