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Perturbations of nuclear$C$*-algebras

Erik Christensen Department of Mathematical Sciences, University of Copenhagen Allan M. Sinclair School of Mathematics, University of Edinburgh Roger R. Smith Department of Mathematics, Texas A&M University Stuart A. White School of Mathematics and Statistics, University of Glasgow Wilhelm Winter Mathematisches Institut, Universität Münster

Spectral Theory and Operator Algebra mathscidoc:1701.32002

Acta Mathematica, 208, (1), 93-150, 2009.10
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.
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@inproceedings{erik2009perturbations,
  title={Perturbations of nuclear$C$*-algebras},
  author={Erik Christensen, Allan M. Sinclair, Roger R. Smith, Stuart A. White, and Wilhelm Winter},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203358035792751},
  booktitle={Acta Mathematica},
  volume={208},
  number={1},
  pages={93-150},
  year={2009},
}
Erik Christensen, Allan M. Sinclair, Roger R. Smith, Stuart A. White, and Wilhelm Winter. Perturbations of nuclear$C$*-algebras. 2009. Vol. 208. In Acta Mathematica. pp.93-150. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203358035792751.
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