JournalsprimsVol. 42, No. 3pp. 691–704

A Similarity Degree Characterization of Nuclear <em>C</em><sup>∗</sup>-algebras

  • Gilles Pisier

    Texas A&M University, College Station, USA
A Similarity Degree Characterization of Nuclear <em>C</em><sup>∗</sup>-algebras cover
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Abstract

We show that a _C_∗-algebra A is nuclear iff there is a number α < 3 and a constant K such that, for any bounded homomorphism u : AB(H), there is an isomorphism ξ : HH satisfying ‖ξ−1‖ ‖ξ‖ ≤ Ku‖α and such that ξ−1 u(.)ξ is a ∗-homomorphism. In other words, an infinite dimensional A is nuclear iff its length (in the sense of our previous work on the Kadison similarity problem) is equal to 2.

Cite this article

Gilles Pisier, A Similarity Degree Characterization of Nuclear <em>C</em><sup>∗</sup>-algebras. Publ. Res. Inst. Math. Sci. 42 (2006), no. 3, pp. 691–704

DOI 10.2977/PRIMS/1166642155