Are locally reflexive C*-algebras exact?

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Source: Conjectured by E. Kirchberg, as reported by N. P. Brown (2006); listed as C*.2 in J. Peterson, Open problems in operator algebras (version of 15 May 2026).

Imported from math.uwaterloo.ca/~j37peter/problems.html.

Classification

Primary

OA — Operator Algebras

Keywords

C*-algebras, exactness, local reflexivity, Peterson's operator algebra problems

Literature checked

Oct. 26, 2026 by clemens-admin

References

@article{brown2006,
  author  = {Brown, Nathanial P.},
  title   = {Invariant means and finite representation theory of {C}$^*$-algebras},
  journal = {Mem. Amer. Math. Soc.},
  volume  = {184},
  number  = {865},
  year    = {2006},
  doi     = {10.1090/memo/0865},
}
@misc{peterson-cs2,
  author       = {Peterson, Jesse},
  title        = {Open problems in operator algebras},
  howpublished = {Web page},
  year         = {2026},
  url          = {https://www.math.uwaterloo.ca/~j37peter/problems.html},
  note         = {Problem C*.2; version of 15 May 2026},
}
@article{kirchberg1995,
  author  = {Kirchberg, Eberhard},
  title   = {On subalgebras of the {CAR}-algebra},
  journal = {J. Funct. Anal.},
  volume  = {129},
  number  = {1},
  pages   = {35--63},
  year    = {1995},
  doi     = {10.1006/jfan.1995.1041},
}
@article{effros1985,
  author  = {Effros, Edward G. and Haagerup, Uffe},
  title   = {Lifting problems and local reflexivity for {C}$^*$-algebras},
  journal = {Duke Math. J.},
  volume  = {52},
  number  = {1},
  pages   = {103--128},
  year    = {1985},
  doi     = {10.1215/S0012-7094-85-05207-X},
}

Citing this problem

This identifier is permanent. It will not change if the problem is solved, reclassified or withdrawn.

OP-00980, "Are locally reflexive C*-algebras exact?", clopen.solutions.