A Note on Approximately Divisible C$^*$-algebras

Details A Note on Approximately Divisible C$^*$-algebras A Note on Approximately Divisible C$^*$-algebras

2008-04-03

arxiv.org/abs/0804.0465v2

Mathematics

Operator Algebras

Scientific paper

Let $\mathcal A$ be a separable, unital, approximately divisible C$^*$-algebra. We show that $\mathcal A$ is generated by two self-adjoint elements and the topological free entropy dimension of any finite generating set of $\mathcal A$ is less than or equal to 1. In addition, we show that the similarity degree of $\mathcal A$ is at most 5. Thus an approximately divisible C$^*$-algebra has an affirmative answer to Kadison's similarity problem.

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