arXiv 0804.04652008-04-21math.OA

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

Weihua Li, Junhao Shen

英文摘要：

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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