Published online by Cambridge University Press: 27 June 2013
We define the class of weakly approximately divisible unital ${C}^{\ast } $-algebras and show that this class is closed under direct sums, direct limits, any tensor product with any
${C}^{\ast } $-algebra, and quotients. A nuclear
${C}^{\ast } $-algebra is weakly approximately divisible if and only if it has no finite-dimensional representations. We also show that Pisier’s similarity degree of a weakly approximately divisible
${C}^{\ast } $-algebra is at most five.