1999/07/11 by Gilles Pisier, Pisier, Gilles
Mathematics · #47D25 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:47D25
paper · pdf · doi:10.48550/arxiv.math/9907062
plain TeX, 33 pages, To appear in Math. Z
arxiv created 1999/07/11 · arxiv updated 2009/11/30
For every integer d≥ 1, there is a unital closed subalgebra Ad⊂ B(H) with similarity degree equal precisely to d, in the sense of our previous paper. This means that for any unital homomorphism u\colon Ad→ B(H) we have ‖u‖cb ≤ K‖u‖d with K>0 independent of u, and the exponent d in this estimate cannot be improved. The proof that the degree is larger than d-1 crucially uses an upper bound for the norms of certain Gaussian random matrices due to Haagerup and Thorbjørnsen. We also include several complements to our previous publications on the same subject.