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The microstates free entropy dimension of any DT–operator is 2. (English) Zbl 1094.46038

Summary: Suppose that \(\mu\) is an arbitrary Borel measure on \(\mathbb C\) with compact support and \(c >0\). If \(Z\) is a DT\((\mu,c)\)-operator as defined by K. Dykema and U. Haagerup in [Am. J. Math. 126, No. 1, 121–189 (2004; Zbl 1054.47026)], then the microstates free entropy dimension of \(Z\) is \(2\).

MSC:

46L54 Free probability and free operator algebras
28A78 Hausdorff and packing measures

Citations:

Zbl 1054.47026
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