The similarity degree of an operator algebra II

Details The similarity degree of an operator algebra II The similarity degree of an operator algebra II

1999-07-11

arxiv.org/abs/math/9907062v1

Mathematics

Operator Algebras

plain TeX, 33 pages, To appear in Math. Z

Scientific paper

For every integer $d\ge 1$, there is a unital closed subalgebra $A_d\subset B(H)$ with similarity degree equal precisely to $d$, in the sense of our previous paper. This means that for any unital homomorphism $u\colon A_d\to B(H)$ we have $\|u\|_{cb} \le K\|u\|^d$ 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 Thorbj\o rnsen. We also include several complements to our previous publications on the same subject.

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