Topological free entropy dimension in unital C∗-algebras

The notion of topological free entropy dimension of n-tuple of elements in a unital C∗ algebra was introduced by Voiculescu. In the paper, we compute topological free entropy dimension of one self-adjoint element and topological free orbit dimension of one self-adjoint element in a unital C∗ algebra. We also calculate the values of topological free entropy dimensions of any families of self-adjoint generators of some unital C∗ algebras, including irrational rotation C∗ algebra, UHF algebra, and minimal tensor product of two reduced C∗ algebras of free groups. © 2009 Elsevier Inc. All rights reserved