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THE SIMILARITY DEGREE OF SOME
${C}^{\ast } $-ALGEBRAS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 89 / Issue 1 / February 2014
- Published online by Cambridge University Press:
- 27 June 2013, pp. 60-69
- Print publication:
- February 2014
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- Article
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- You have access
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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.
