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 : A → B(H), there is an isomorphism ξ : H → H satisfying ‖ξ−1‖ ‖ξ‖ ≤ K ‖u‖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. 691–704DOI 10.2977/PRIMS/1166642155